Question

If f(x) = x2 -1, what is the equation for f¹(x)?

Answer 1

Given

`f(x)=x^2-1`

To find the inverse of f(x).

Step-by-step explanation:

It is given that,

`f(x)=x^2-1`

Step 1:

Put f(x)=y.

That implies,

`y=x^2-1`

Step 2:

Replace x by y.

That implies,

`x=y^2-1`

Step 3:

Solve for y.

That implies,

`\begin{gathered} y^2=x+1 \\ y=\pm√(x+1) \end{gathered}`

Hence,

`f^(-1)(x)=\pm√(x+1)`