Question

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

Answer 1

Answer:

$f^{-1} = \frac{ 7(x-4)}{2}$

Step-by-step explanation:

Given

$f(x) = \frac{2x}{7} + 4$

Required

The inverse function

$f(x) = \frac{2x}{7} + 4$

Replace f(x) with y

$y = \frac{2x}{7} + 4$

Swap x and y

$x = \frac{2y}{7} + 4$

Multiply through by 7

$7x = 2y + 28$

Solve for 2y

$2y = 7x - 28$

Solve for y

$y = \frac{ 7x-28}{2}$

Factorize

$y = \frac{ 7(x-4)}{2}$

Write as:

$f^{-1} = \frac{ 7(x-4)}{2}$