Question

Find f^-1(x)

A
B
C
D

Answer 1

Choice d is the answer.

Step-by-step explanation:

We have given a function.

f(x) = 1/2x-5

We have to find the inverse of the function.

f⁻¹(x) = ?

Putting y = f(x) in given equation, we have

y = 1/2x-5

Separating x , we have

y+5 = 1/2x

x = 2(y+5)

Putting x = f⁻¹(y) in above equation, we have

f⁻¹(y) = 2y+10

Replacing y by x , we have

f⁻¹(x) = 2x+10 which is the answer.

Answer 2

D. f⁻¹(x) = 2x + 10

Step-by-step explanation:

The given is:

`f(x) = (1)/(2)x - 5`

To find the inverse, follow the below procedures:

1- Convert f(x) to y.

This will give:

`y = (1)/(2) x - 5`

2- Swap the x and y variables.

This will give:

`x = (1)/(2)y - 5`

3- Solve for y.

This will give:

`x = (1)/(2)y - 5\\ \\ (1)/(2)y = x+5\\ \\ y = 2x+10`

4- Replace the y in the above step with f⁻¹(x).

This will give us:

f⁻¹(x) = 2x + 10

Hope this helps :)