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3.2 Algebra and Functions (A-level only)

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Question 39

The function f f\,f is defined by

f(x)=1x+5,x∈R,x≠−5 f(x) = \frac{1}{x+5}, \quad x \in \mathbb{R}, x \neq -5 f(x)=x+51​,x∈R,x=−5 g(x)=3x2−1,x∈R g(x) = 3x^2 - 1, \quad x \in \mathbb{R} g(x)=3x2−1,x∈R
a.

Write down the range of f(x)f(x)f(x)

[2]
b.

Find an expression for f−1(x)f^{-1}(x)f−1(x) and state its domain

[3]
c.

Solve fg(x)=116\displaystyle fg(x) = \frac{1}{16}fg(x)=161​

[3]

3.2 Algebra and Functions (A-level only) Questions

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