Answer:
Inverse of [tex]f(x)=x^2-16[/tex] is [tex]f^{-1}(x)=\sqrt{x+16}[/tex]
Option A is correct option.
Step-by-step explanation:
We need to find inverse of [tex]f(x)=x^2-16[/tex]
For finding inverse replace f(x) with y
[tex]y=x^2-16[/tex]
Now, solve for x
Adding 16 on both sides
[tex]y+16=x^2-16+16\\y+16=x^2\\=> x^2=y+16[/tex]
Taking square root on both sides:
[tex]x^2=y+16\\\sqrt{x^2} =\sqrt{y+16} \\x=\sqrt{y+16}[/tex]
Now replace x with f^{-1}(x) and y with x
[tex]f^{-1}(x)=\sqrt{x+16}[/tex]
So, inverse of [tex]f(x)=x^2-16[/tex] is [tex]f^{-1}(x)=\sqrt{x+16}[/tex]
Option A is correct option.
