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3.2.3 Algebra and Functions (A-level only)

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Question 46

The functions fff and ggg are defined by

f(x)=16−x2x∈R,x≥0 f(x) = 16 - x^2 \quad x \in \mathbb{R}, x \ge 0 f(x)=16−x2x∈R,x≥0 g(x)=43x+2x∈R,x≥0 g(x) = \frac{4}{3x + 2} \quad x \in \mathbb{R}, x \ge 0 g(x)=3x+24​x∈R,x≥0
a.

Write down the range of fff.

[1]
b.

Find the value of fg(2)fg(2)fg(2).

[2]
c.

Find g−1(x)g^{-1}(x)g−1(x) and state its domain.

[4]

3.2.3 Algebra and Functions (A-level only) Questions

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