Question

Which equation is the inverse of y = 9x2 - 4?

x = 2√x +4
V
IVX+4
y=+ V +4
y +Vx+4

Answer 1

The inverse will be:

`y' = (√(x+4))/(3)`

Explanation:

In order to find the inverse of the equation, we do a variable change, since we are finding the inverse, :

`f(x)  = 9x^(2) - 4`

`y = 9x^(2) - 4`

`x = 9y' ^(2) - 4`

Now solve for y'.

First add 4 in both sides of the equation and change to the left y'.

`x + 4= 9y'^(2) - 4+4`

`9y'^(2)` = x + 4

Second divide by 9

`9y'^(2)`/9 = (x + 4)/9

`y'^(2)` = (x + 4)/9

Now you will have to clear y, with the square root.

`[tex]y'^{(2)/(2)} = √(x + 4)  / √(9)`[/tex] =

Simplifying terms

`y' = (√(x+4))/(3)`

`f^(-1)(x)  = (√(x+4))/(3)`

You can check the answer by doing the evaluation of the following equation:

(f o
`f^(-1)` ) (x)

substitute the equation for y' or inverse function
`f^(-1)`

f(
`(√(x+4) )/(3)`)

Now substitue the value into f(x)

You will have

`= 9((√(x+4) )/(3)} )^(2)  - 4\\\\Solving\\\\9(\frac{{x+4} }{9}} )  - 4`

=x