Question

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

o pr}(X) = 7+2
O q'(x) = -2
O 0760) = (+)+2
O 011(x) = (+) --

Answer 1

`g'(x) = (x^2)/(100) +2`

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

`(x)/(10) = \sqrt{y - 2`

Square of both sides

`(x^2)/(100) = y - 2`

Make y the subject

`y = (x^2)/(100) +2`

Replace y with g'(x)

`g'(x) = (x^2)/(100) +2`

Hence, the inverse function is:
`g'(x) = (x^2)/(100) +2`