Question

If F(x) = +4, which of the following is the inverse of Fx)?

O A. F^1(x) = 2(x-4)
O B. F^1(x) = 7(x+4)
O C.F^1(x) = 7(x-4)
D. F1(x) = 2(x+4)​

Answer 1

`f^(-1) = ( 7(x-4))/(2)`

Explanation:

Given

`f(x) = (2x)/(7) + 4`

Required

The inverse function

`f(x) = (2x)/(7) + 4`

Replace f(x) with y

`y = (2x)/(7) + 4`

Swap x and y

`x = (2y)/(7) + 4`

Multiply through by 7

`7x = 2y + 28`

Solve for 2y

`2y = 7x - 28`

Solve for y

`y = ( 7x-28)/(2)`

Factorize

`y = ( 7(x-4))/(2)`

Write as:

`f^(-1) = ( 7(x-4))/(2)`