Question

3.
Which is the inverse of the function f(x) = x2 - 4?

Answer 1

`\boxed{\±√(x+4)}`

Explanation:

The inverse of a function is the reverse of the function.

`f(x)=x^2 -4`

`y=x^2-4`

Switch variables.

`x=y^2-4`

Make y as subject.

Add 4 to both sides.

`x+4=y^2`

Take the square root on both sides.

`\±√(x+4) =y`

Answer 2

`f^(-1)` = ±
`√(x+4)`

Explanation:

`f(x) = x^2-4`

Replace f(x) by y

`y = x^2-4`

Exchange x and y

`x = y^2-4`

Solve for y

`x = y^2-4\\`

Adding 4 to both sides

`y ^2 = x+4`

Taking sqrt on both sides

y = ±
`√(x+4)`

Replacing y by
`f^(-1)`

`f^(-1)` = ±
`√(x+4)`