1.7: Exponential composite and inverse sketch

0606/11/O/N/19 — Question 5 · 7 marks

f(x)=3e2x+1f(x) = 3\mathrm{e}^{2x} + 1 for x∈Rx \in \mathbb{R} and g(x)=x+1g(x) = x + 1 for x∈Rx \in \mathbb{R}.
(i)
Write down the range of ff and of gg.
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(ii)
Evaluate fg2(0)fg^{2}(0).
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(iii)
On the axes below, sketch the graphs of y=f(x)y = f(x) and y=f−1(x)y = f^{-1}(x), stating the coordinates of the points where the graphs meet the coordinate axes.
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