Composition with an inverse and intersections of a function and its inverse
Work with the inverse rule on the exact domain stated below
The function \(f\) is defined by the rule
\[f(x)=\frac{1}{2}x+\frac{3}{2}\]
with domain \(\left[-1,\;7\right]\)
The inverse rule is
\[f^{-1}(x)=\frac{x-\frac{3}{2}}{\frac{1}{2}}\]
The domain of \(f^{-1}\) is \(\left[1,\;5\right]\)
The composition to use is \(f\left(f^{-1}(x)\right)\). The probe input is \(5\)