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
[tex]y^2=\frac{1}{9}(x + 12)[/tex]
[tex]y=\pm\sqrt{\frac{1}{9}(x + 12)}[/tex]
[tex]y=\pm\frac{\sqrt{(x+12)}}{3}[/tex] Here, x > -12
Step 4,
Covert this equation into function,
[tex]g(x)=\pm\frac{\sqrt{(x+12)}}{3}[/tex]
Therefore, Option C will be the answer.
