Question

Which function is the inverse of function f?

Answer 1

Answer:

Option D is correct.

Step-by-step explanation:

f(x)= 9x^2 -12

Let y = 9x^2 - 12

Switch places of x and y and solve for y

x = 9y^2 - 12

Adding 12 on both sides

x + 12 = 9y^2

Dividing both sides by 9

x+12/9 = y^2

=> Taking square root on both sides

=> $\sqrt{y^2}= \sqrt{\frac{x+12}{9}}\\y=\pm\frac{\sqrt{x+12}}{3}$

Replace y with g(x)

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

Option D is correct.

Answer 2

Answer: Option D

$g(x)=\±\frac{\sqrt{x+12}}{3}$  for $x\geq -12$

Step-by-step explanation:

We have the following function

$f(x) = 9x^2-12$

make $f (x) = y$

$y = 9x^2-12$

To find the inverse of the function, solve for the variable x

$y+12 = 9x^2$

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

$x=\±\sqrt{\frac{y+12}{9}}$

$x=\±\frac{\sqrt{y+12}}{3}$

Now interchange the variable x with the variable y

$y=\±\frac{\sqrt{x+12}}{3}$  for $x\geq -12$

Finally, make g(x) = y

$g(x)=\±\frac{\sqrt{x+12}}{3}$  for $x\geq -12$