Answer:
Option C
Step-by-step explanation:
Given function is,
f(x) = 9x² - 12
Steps to find the inverse of the given function,
Step 1,
Write the function in the form of an equation,
y = 9x² - 12
Step 2,
Interchange variables 'x' and 'y' in the equation,
x = 9y² - 12
Step 3,
Solve this equation for 'y',
x = 9y² - 12
9y² = x + 12
![y^2=\frac{1}{9}(x + 12)](https://tex.z-dn.net/?f=y%5E2%3D%5Cfrac%7B1%7D%7B9%7D%28x%20%2B%2012%29)
![y=\pm\sqrt{\frac{1}{9}(x + 12)}](https://tex.z-dn.net/?f=y%3D%5Cpm%5Csqrt%7B%5Cfrac%7B1%7D%7B9%7D%28x%20%2B%2012%29%7D)
Here, x > -12
Step 4,
Covert this equation into function,
![g(x)=\pm\frac{\sqrt{(x+12)}}{3}](https://tex.z-dn.net/?f=g%28x%29%3D%5Cpm%5Cfrac%7B%5Csqrt%7B%28x%2B12%29%7D%7D%7B3%7D)
Therefore, Option C will be the answer.