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1.5.8 Composite and inverse functions (A-level only)

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Question 3
56%

The function f f\,f is defined by

f(x)=1x−1,x∈R,x≠1 f(x) = \frac{1}{x-1}, \quad x \in \mathbb{R}, x \neq 1 f(x)=x−11​,x∈R,x=1 g(x)=x2−4,x∈R g(x) = x^2 - 4, \quad x \in \mathbb{R} g(x)=x2−4,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)=14\displaystyle fg(x) = \frac{1}{4}fg(x)=41​

[3]

1.5.8 Composite and inverse functions (A-level only) Questions

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