1.8: Logarithmic inverse and sketch

0606/11/O/N/20 — Question 7 · 9 marks

It is given that f(x)=5ln⁡(2x+3)f(x) = 5\ln(2x + 3) for x>−32x > -\tfrac{3}{2}.
(a)
Write down the range of ff.
[1]
(b)
Find f−1f^{-1} and state its domain.
[3]
(c)
On the axes below, sketch the graph of y=f(x)y = f(x) and the graph of y=f−1(x)y = f^{-1}(x). Label each curve and state the intercepts on the coordinate axes.
[5]