Question

For the function g(x) = 10 VX-2, what is the inverse function?

Answer 1

Answer:

$g'(x) = \frac{x^2}{100} +2$

Step-by-step explanation:

Given

$g(x) = 10\sqrt{x - 2$

Required

Determine the inverse function

$g(x) = 10\sqrt{x - 2$

Replace g(x) with y

$y = 10\sqrt{x -2$

Swap the positions of x and y

$x = 10\sqrt{y -2$

Divide through by 10

$\frac{x}{10} = \sqrt{y - 2$

Square of both sides

$\frac{x^2}{100} = y - 2$

Make y the subject

$y = \frac{x^2}{100} +2$

Replace y with g'(x)

$g'(x) = \frac{x^2}{100} +2$

Hence, the inverse function is: $g'(x) = \frac{x^2}{100} +2$