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Functions and Graphs

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Question 118

The function f f\,f is defined by

f(x)=1x+3,x∈R,x≠−3 f(x) = \frac{1}{x+3}, \quad x \in \mathbb{R}, x \neq -3 f(x)=x+31​,x∈R,x=−3
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.

g(x)=x2−6,x∈Rg(x) = x^2 - 6, \quad x \in \mathbb{R}g(x)=x2−6,x∈R

Given that fg(x)=1x2−3\displaystyle fg(x) = \frac{1}{x^2-3}fg(x)=x2−31​, solve fg(x)=12\displaystyle fg(x) = \frac{1}{2}fg(x)=21​

[2]
Markscheme

Functions and Graphs Questions

  1. A Level
  2. /Maths
  3. /Functions and Graphs

471 exam-style questions on Edexcel A Level Maths Functions and Graphs, covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems. Each one has a worked solution and a mark scheme showing where the marks go.

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