Question

Which function is the inverse of f

Answer 1

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

$y^2=\frac{1}{9}(x + 12)$

$y=\pm\sqrt{\frac{1}{9}(x + 12)}$

$y=\pm\frac{\sqrt{(x+12)}}{3}$ Here, x > -12

Step 4,

Covert this equation into function,

$g(x)=\pm\frac{\sqrt{(x+12)}}{3}$

Therefore, Option C will be the answer.