Composition with an inverse and intersections of a function and its inverse
Solve the required equation algebraically and check the stated domain
The function \(q\) is defined by the rule
\[q(x)=2x+3\]
with domain \(\left[-7,\;1\right]\)
The inverse rule is
\[q^{-1}(x)=\frac{x-3}{2}\]
The domain of \(q^{-1}\) is \(\left[-11,\;5\right]\)
The composition to use is \(q^{-1}\left(q(x)\right)\). The probe input is \(-7\)