Answers
Answer:
f(2) = -6
f inverse of 1/2 is 17/2
Step-by-step explanation:
We are given a function [tex]\displaystyle \large{f(x) = \frac{6}{2x-5}}[/tex]
To solve for part (a), we have to substitute x = 2 in f(x).
[tex]\displaystyle \large{f(2)=\frac{6}{2(2)-5} \\\displaystyle \large{f(2)=\frac{6}{4-5}=\frac{6}{-1}=-6[/tex]
Therefore, f(2) is -6.
Now we solve for part (b), we see the notation which is a minor different similar to f(x). We see that there is exponent of -1 between f and 1/2. The part (b) indicates that the function is an inverse of f(x).
[tex]\displaystyle \large{y=f^{-1}(x) \longrightarrow x=f(y)}[/tex]
To solve for part (b), first we solve for x in the function. Let f(x) = y.
[tex]\displaystyle \large{y=\frac{6}{2x-5}}[/tex]
Multiply both sides by 2x-5.
[tex]\displaystyle \large{y(2x-5)=\frac{6}{2x-5}(2x-5)}\\\displaystyle \large{y(2x-5)=6}[/tex]
Divide both sides by y-term.
[tex]\displaystyle \large{\frac{y(2x-5)}{y}=\frac{6}{y}}\\\displaystyle \large{2x-5=\frac{6}{y}}\\\displaystyle \large{2x=\frac{6}{y}+5}\\\displaystyle \large{x=\frac{6}{2y}+\frac{5}{2}}\\\displaystyle \large{x=\frac{3}{y}+\frac{5}{2}}[/tex]
Then swap x and y which we receive [tex]\displaystyle \large{y=\frac{3}{x}+\frac{5}{2}}[/tex]
Therefore, [tex]\displaystyle \large{f(x)=\frac{6}{2x-5} \longrightarrow f^{-1}(x)=\frac{3}{x}+\frac{5}{2}}[/tex]
Thus, [tex]\displaystyle \large{f^{-1}(\frac{1}{2})=\frac{3}{\frac{1}{2}}+\frac{5}{2}}\\\displaystyle \large{f^{-1}(\frac{1}{2})=6+\frac{5}{2}}\\\displaystyle \large{f^{-1}(\frac{1}{2})=\frac{17}{2}}[/tex]
____________________
Let me know if you have any questions in comment.
Related Questions
if 2-5 = -4 then x =
please answer
Answers
Answer:
1
Step-by-step explanation:
2-5=x-4
subtract the common factors
-3 = x-4
add 4 to both sides so get x by itself
1 = x
Shameka buys a blue garden hose that is 16.5 feet long and a green garden hose that is 14.75 feet long. How many feet of garden hose does she buy?
Help please?
Answers
Answer:
21.25 feet
Step-by-step explanation:
16.5 feet
+14.75
=21.25 feets
Write an equation that reflects this relationship using x to represent the amount of fish in grams and y to represent the number of calories.
Answers
Answer:
send the graph and ill solve it
Step-by-step explanation:
Find two numbers that round to 387.4 when rounded to the nearest tenth. Drag the numbers to the box.
Answers
Answer: By using the rounding rule.
Step-by-step explanation:
387 x 397 => 387.4
384 x 352 => 387.4
Colin invests £2350 into a savings account. The bank gives 4.2% compound
interest for the first 4 years and 4.9% thereafter. How much will Colin have after
10 years to the nearest pound?
Answers
Answer:
Answer:
£3692
Step-by-step explanation:
A = p(1 + r/n)^nt
Where,
A = future value
P = principal = £2350
r = interest rate = 4.2% = 0.042
n = number of periods = 1(annual)
t = time = 4 years
A = p(1 + r/n)^nt
= 2350(1 + 0.042/1)^1*4
= 2350(1 + 0.042)^4
= 2350(1.042)^4
= 2350(1.5789)
= 2770.42
A = £2770.42
Total years = 10
Remaining years = 10 – 4
= 6 years
Remaining 6 years
P = £2770.42
r = 4.9% = 0.049
n = 1
t = 6
A = p(1 + r/n)^nt
= 2770.42(1 + 0.049/1)^1*6
= 2770.42(1 + 0.049)^6
= 2770.42(1.049)^6
= 2770.42(1.3325)
= 3691.59
A = £3691.59
Approximately £3692
Thank you!
Kashira has 3/9 of a pizza and Laila gave her 1/3 of a pizza. How much pizza does Kashira have now? Please provide your answer in simplest form. (NVM FIGURED IT OUT)
Answers
Answer:4/9 pizzas
Step-by-step explanation:
A local volunteer group has 150 raffle tickets to sell. They sell them in packs of three tickets per customer. Determine which graph and which equation represent the number of tickets, T, the group has left after selling tickets to c customers.
Answers
The equation that represents the number of tickets T, the group has left after selling tickets to c customers is:
T = 150 - 3c
The graph representing the equation is plotted below
The total number of tickets that the volunteer group has = 150
They sell the tickets in packs of three tickets per customer
The number of customers is c
Number of tickets sold to c customers = 3c
The number of tickets left after selling tickets to c customers is:
T = 150 - 3c
Learn more here: https://brainly.com/question/25912293
Answer:
I HAVE COME TO SAVE THE DAY!
ok the equation is t= -3c + 150
the graph is the one that is the same as the equation the y intercept is 150 the slope is -3 over 1 (up three over one) on y test the answers were the top right for both boxes but it might be different for you
James is planning to spend $425 on food for his vacation this summer. This is 34% of his total vacation budget. How much is James' total vacation budget?
Answers
1250$,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
1.) Jacob bought a total of 9 pizzas for his class party. The amount of
large pizzas was twice the amount of medium pizzas. How many large
and how many medium pizzas did he buy?
Equation #1:
Equation #2:
Large Pizzas:
Medium Pizzas:
what’s the equations
Answers
Answer:
Equation 1: L+M=T
Equation 2: 2M=L
Large Pizzas: 6 pizzas
Medium Pizzas: 3 Pizza
Step-by-step explanation:
Equation 1 looks like L+M=T where L is large pizza, M is medium pizza and T is Total of pizzas. The second one would look like 2M=L, to represent how twice the amount of medium pizza equal large pizza. If you were using different variables it would look like X+Y=Total, and 2X=Y.
a/m = b + c i need to make “a” the subject of the formula
Answers
hope it helped !
What is the approximate value of x?
Answers
Answer:
25
Step-by-step explanation:
Answer: The answer is 25.
Have a great Day/Night!
What is the approximate value of t?
Answers
Answer:
8.48
Step-by-step explanation:
36 + 36 = 72
t^2 = 72
t = 6[tex]\sqrt{2}[/tex] = 8.48
Answer: 6
Step-by-step explanation:
SOMEONE HELP!!!!!!!!!!!!!!!!!!!! I would give more points but there are people who just write random things for an answers that isnt correct just to get points.
Answers
Answer:
a) 320 is correct
b) 20 more 18 year old students
Step-by-step explanation:
a) 320 is correct
b) 20 more 18 year old students: The only information we have in the 25 - 35 minute time frame is the data for 30 minutes:
12 years: 40 students
18 years: 60 students
Difference = 20 more 18 year old students than 12 year old students spent spent time on social media for 25 - 35 seconds.
Someone please help me with this it’s an emergency
Answers
Answer:
The answers are given in the photo
_________________ help the group manage relationships
a.
Social roles
b.
Leadership roles
c.
Task roles
d.
Individual roles
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
B
Step-by-step explanation:
Leadership roles help the group manage relationships
[] Leadership is the action of leading a group of people or an organization, so this best completest the answer
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
x²+1=2x
hope someone can help thanks!
Answers
Answer:
I think it’s x=1
Answer:
Step-by-step explanation:
x^2 + 1 = 2x
x^2 - 2x + 1 = 0
Factor (x - 1) ( x - 1)
x = 1
help help help help help help help help
Answers
Answer:
necklace
Step-by-step explanation:
It is the only one with a negative elevation
help plzz) A teacher made a copy of a map. To make the map easier to see, the teacher enlarged the area of the map by 38%. Let d represent the area of the original map. The expression d +0.38d is one way to represent the area of the new map. Write two expressions that represent the area of the new map.
Answers
Answer:
first expressions = 1.38d
second expressions = (1 + (38/100)d
Miss Watson runs a distance of 200 meters in 25 seconds.
Work out the average speed of Miss Watson in meters per second?
Answers
Step-by-step explanation:
D = 200m T = 25s
The formula for speed is speed = distance ÷ time
S = 200 ÷ 25
S = 8m/s
#6 Solve the inequality.
6w <-42
Answers
Answer:
w < -7
Step-by-step explanation:
Do -42 divided by 6 and keep the sign the same.
You get w < -7.
Hope this helps! :)
Baby Deirdre wants to arrange 8 blocks in a row. How many different arrangements can the baby make?
There are
ways to arrange the 8 blocks.
Answers
Sonal and Gaurav have 2 numbers written on a piece of paper. Sonal's number PQR is divisible by
3 and 4. Gaurav's number STU is divisible by 2 and 9.
The two numbers are joined to form a new 6-digit number PQRSTU as shown.
The number PQRSTU IS DEFINITELY divisible by
A 4 B 6 с 8 D 9
Answers
PQRSTU is definitely divisible by 4.
Since Sonal and Gaurav have 2 numbers written on a piece of paper, and Sonal's number PQR is divisible by 3 and 4, while Gaurav's number STU is divisible by 2 and 9, and the two numbers are joined to form a new 6- digit number PQRSTU, to determine the number by which the number PQRSTU is definitely divisible by, the following logical reasoning must be performed:
Since the numbers are not added mathematically, but joined numerically, and that STU is the last number in the row, and that it is divisible by 3 and 4, while only 4 is among the options, the number PQRSTU is definitely divisible by 4.
Learn more about maths in https://brainly.com/question/20010402
-2x(-3x +2)- (x+2)2
giúp tôi với!
Answers
Answer:
-32 or 4x -8
Step-by-step explanation:
-2 ( -3x + 2 ) : 6x - 4
= 6x -4 - 2 ( x + 2 )
- 2 ( x + 2 ) : - 2x -4
=6x - 4 - 2x - 4
= 6x -2x - 4 - 4
= 6x - 2x - 8
= 4x - 8
= -32
( Im not really sure what is the answer )
( the "x" is alphabet, not "times" )
True or false: (log x)2 = 2logx. Explain your thinking.
Answers
Well we can’t put 2 log x it’s opposite it’s 2 x log
Find x, given the slope is -2. (x,-6) (-6,10)
Answers
Answer:
x= 2
Step-by-step explanation:
[tex]\boxed{slope = \frac{y _{1} - y_2}{x_1 - x_2} }[/tex]
Substitute known values into the formula:
[tex] - 2 = \frac{ - 6 - 10}{x - ( - 6)} [/tex]
[tex] - 2 = \frac{ - 16}{x + 6} [/tex]
-2(x +6)= -16
Divide both sides by -2:
x +6= -16 ÷(-2)
x +6= 8
Subtract both sides by 6:
x= 8 -6
x= 2
Please help I’ll give brainliest ASAP
Answers
Answer:
x = 10, theta = 30 degrees
Step-by-step explanation:
i. 6^2 + 8^2 = x^2
36 + 64 = x^2
100 = x^2
10 = x
ii. the angle is 30 degrees, because the opposite side is 1/2 of the hypotenuse.
You could also solve it with the law of sines:
sin(90)/12 = sin(x)/6
Multiply each side by 6
6 * sin(90)/12 = sin(x)
0.5 = sin(x)
x = 30 degrees
Work out m and c for the line:3x + 2y−1 =0
please help quickly
Answers
Answer:
m=-1.5 and c=0.5
Step-by-step explanation:
3x+2y-1=0
divide everything by 2, to get y.
3x/2=1.5x, -1/2=-0.5.
then separate 1.5x and -0.5 from y (put them on the other side)
there, y=-1.5x+0.5
m=-1.5, and c=0.5
✺༒Question༒✺
Refer to attachment
Nonsence answer will get report
Answers
Answer:
Hey mate.....
Step-by-step explanation:
This is ur answer.....
(i) 64(ii) 729(iii) 121(iv) 625Hope it helps!
Brainliest pls!
Follow me! :)
Answer:
REFER TO ATTACHMENT
I HOPE IT IS HELPFULEstimate the product. Then find the actual product
483 x 9.3
please label the actual product and the estimate
Answers
Actual Product:
4491.9
Estimated Product:
4492
How is it 4492?
4491.9
The 9 is greater than 5 making it go up,
aka, making the 1 turn into a 2.
evaluate the expression.
Answers
Answer:
The value of [tex](-25)^{\frac{1}{2} }=5i[/tex]
Step-by-step explanation:
We need to find [tex](-25)^{\frac{1}{2} }[/tex]
We have
[tex](-25)^{\frac{1}{2} }=\sqrt{-25} \\\\=\sqrt{25} \times\sqrt{-1} \\\\=5 i[/tex]