Question

For the function f(x) = (4 – 2x)^2, find f^–1 and the domain and range of f and f^–1. Determine whether f^–1 is a function.

Answer 1

\[f(x)=(4-2x)^2\] is not a one to one function, so the inverse is not a function
in fact you cannot write \(f^{-1}(x)\) because that presupposes it is a funciton
you can however write
\[x=(4-2y)^2\] and solve for \(y\)

Answer 2

\[x=(4-2y)^2\]
\[\pm\sqrt{x}=4-2y\]
\[\pm\sqrt{x}-4=-2y\]
\[y=\frac{\pm\sqrt{x}}{2}+2\]