Answer:
The inverse function is g(x) = ± [tex]\frac{\sqrt{x+12}}{3}[/tex] , x ≥ -12 ⇒ D
Step-by-step explanation:
* Lets explain how to find the inverse function
- The steps of find the inverse of function f(x)
# Write y = f(x)
# Switch x and y
# Solve to find the new y
* Lets solve the problem
∵ f(x) = 9x² - 12
- Do the steps above
- Put y = f(x)
∵ y = f(x)
∴ y = 9x² - 12
- Switch x and y
∴ x = 9y² - 12
- Add both sides by 12
∴ x + 12 = 9y²
- take √ for both side don't forget to put ± in-front of it
∴ ± [tex]\sqrt{x+12}[/tex] = 3y
- Divide both sides by 3
∴ y = ± [tex]\frac{\sqrt{x+12}}{3}[/tex]
∵ There is no square root for negative number
∴ x + 12 ≥ 0 ⇒ subtract 12 from both sides
∴ x ≥ -12
- The function is defined for all values of x greater than or equal -12
∴ The inverse function is g(x) = ± [tex]\frac{\sqrt{x+12}}{3}[/tex] , x ≥ -12
