Given:
The function is:
[tex]f(x)=x^2-16[/tex]
To find:
The inverse of the function.
Solution:
We have,
[tex]f(x)=x^2-16[/tex]
Step 1: Substitute [tex]f(x)=y[/tex].
[tex]y=x^2-16[/tex]
Step 2: Interchange x and y.
[tex]x=y^2-16[/tex]
Step 3: Isolate y.
[tex]x+16=y^2[/tex]
[tex]\pm \sqrt{x+16}=y[/tex]
[tex]y=\pm \sqrt{x+16}[/tex]
Step 4: Substitute [tex]y=f^{-1}(x)[/tex].
[tex]f^{-1}(x)=\pm \sqrt{x+16}[/tex]
Therefore, the inverse function of the given function is [tex]f^{-1}(x)=\pm \sqrt{x+16}[/tex].
