Question

Find the inverse of the function ( ) 2 5g x x= − + . SHOW ALL WORK

Answer 1

g⁻¹(x) = 2 - √x + 5

Explanation:

g(x) = 2 - √x + 5

g⁻¹(x) = ?

the steps to find the inverse of a function are as follows:

step 1: let g(x) = y

y = 2 - √x + 5

step 2: sway x and y

x = 2 - √y + 5

step 3: solve for y

√y + 5 = 2 - x

y + 5 = (2 - x)²

y = (-x + 2)² - 5

= x² + 4 - 4x - 5

= x² - 4x - 1

thus, inverse of a function is:

g⁻¹(x) = x² - 4x - 1