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3.1 Algebra and functions (A-level only)

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Question 50

The function f f\,f is defined by

f(x)=4x+3,x∈R,x≠−3 f(x) = \frac{4}{x+3}, \quad x \in \mathbb{R}, x \neq -3 f(x)=x+34​,x∈R,x=−3 g(x)=x2−2,x∈R g(x) = x^2 - 2, \quad x \in \mathbb{R} g(x)=x2−2,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)=1fg(x) = 1fg(x)=1

[3]

3.1 Algebra and functions (A-level only) Questions

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