Given
[tex]f(x)=x^2-1[/tex]
To find the inverse of f(x).
Explanation:
It is given that,
[tex]f(x)=x^2-1[/tex]
Step 1:
Put f(x)=y.
That implies,
[tex]y=x^2-1[/tex]
Step 2:
Replace x by y.
That implies,
[tex]x=y^2-1[/tex]
Step 3:
Solve for y.
That implies,
[tex]\begin{gathered} y^2=x+1 \\ y=\pm\sqrt{x+1} \end{gathered}[/tex]
Hence,
[tex]f^{-1}(x)=\pm\sqrt{x+1}[/tex]
