4.04: Inverse and composite functions
\(f(x)=1+2^x\) for \(x\geqslant-1\).
(a)[1]
State the range of \(f\).
See the official mark scheme below.
(b) (i)[1]
State the domain of \(f^{-1}\).
See the official mark scheme below.
(b) (ii)[2]
Find \(f^{-1}(x)\).
See the official mark scheme below.
(b) (iii)[4]
On the same axes, sketch \(y=f(x)\) and \(y=f^{-1}(x)\), giving intercepts.
See the official mark scheme below.
(c) (i)[1]
\(g(x)=x(x+k)\) for \(x\geqslant-1\). Explain why \(gf\) exists.
See the official mark scheme below.
(c) (ii)[1]
Find \(gf(x)\).
See the official mark scheme below.
(c) (iii)[2]
Given that \(gf(3)=126\), find \(k\).
See the official mark scheme below.
