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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 278

The functions fff and ggg are defined by

f(x)=3+4ln⁡x,x>0 f(x) = 3 + 4\ln x, \quad x > 0 f(x)=3+4lnx,x>0 g(x)=8x−42x+1,x>12 g(x) = \frac{8x - 4}{2x + 1}, \quad x > \frac{1}{2} g(x)=2x+18x−4​,x>21​
a.

Find f−1(15)f^{-1}(15)f−1(15).

[2]
b.

Use differentiation to prove that ggg is an increasing function.

[3]
c.

Find g−1(x)g^{-1}(x)g−1(x).

[3]
d.

Find the range of the composite function fgfgfg.

[3]
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3 Unit A2 1: Pure Mathematics (A-level only) Questions

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