1.9: Quadratic mapping and logarithmic composite

0606/12/M/J/20 — Question 5 · 9 marks

f:x↦(2x+3)2f : x \mapsto (2x + 3)^{2} for x>0x > 0.
(a)
Find the range of ff.
[1]
(b)
Explain why ff has an inverse.
[1]
(c)
Find f−1f^{-1}.
[3]
(d)
State the domain of f−1f^{-1}.
[1]
(e)
Given that g:x↦ln⁡(x+4)g : x \mapsto \ln(x + 4) for x>0x > 0, find the exact solution of fg(x)=49fg(x) = 49.
[3]