Question

Which function is the inverse of function f?

Answer 1

Answer: Option D

`g(x)=\±(√(x+12))/(3)` for
`x\geq -12`

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=(y+12)/(9)`

`x=\±\sqrt{(y+12)/(9)}`

`x=\±(√(y+12))/(3)`

Now interchange the variable x with the variable y

`y=\±(√(x+12))/(3)` for
`x\geq -12`

Finally, make g(x) = y

`g(x)=\±(√(x+12))/(3)` for
`x\geq -12`

Answer 2

Option D is correct.

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

=>
`√(y^2)= \sqrt{(x+12)/(9)}\\y=\pm(√(x+12))/(3)`

Replace y with g(x)

`g(x)=\pm(√(x+12))/(3)`

Option D is correct.