Answer:
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