4.02: Composite and inverse functions
\(f(x)=3x^2+8x\) for \(x\geqslant k\), and \(f^{-1}\) exists. The value of \(k\) is the least possible.
(a)[2]
Find \(k\).
See the official mark scheme below.
(b)[2]
State the range of \(f\).
See the official mark scheme below.
(c)[3]
Find \(f^{-1}(x)\).
See the official mark scheme below.
(d) (i)[1]
The function \(g\) is defined by \(g(x)=3^x\) for \(x\geqslant-6\). State the domain of \(gf\).
See the official mark scheme below.
(d) (ii)[4]
Solve \(gf(x)=27\).
See the official mark scheme below.
