Question

I need help, plato hates me...

Answer 1

Answer:

The inverse function is g(x) = ± $\frac{\sqrt{x+12}}{3}$ , 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

∴ ± $\sqrt{x+12}$ = 3y

- Divide both sides by 3

∴ y = ± $\frac{\sqrt{x+12}}{3}$

∵ 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) = ± $\frac{\sqrt{x+12}}{3}$ , x ≥ -12