Answer:
[tex]x\leq 4[/tex] or [tex]x\geq 4[/tex]
Step-by-step explanation:
We are given that
[tex]f(x)=(8-2x)^2[/tex]
We have to find the restricted domain of f which make the inverse of f.
Substitute x=4
[tex]f(4)=0[/tex]
One-to-one function:
The function is called one-to-one when
[tex]f(x_1)=f(x_2)[/tex] for [tex]x_1=x_2[/tex]
The function is one-to-one when [tex]x\leq 4[/tex] or [tex]x\geq 4[/tex]
When the function is one-to-one then the function has inverse function.
If the function is not one-to-one then function has no inverse .
Therefore, the restricted domain of f which make the inverse of f(x) a function is given by
[tex]x\leq 4[/tex] or [tex]x\geq 4[/tex]
