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Functions and Graphs

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Question 174

The function f−1f^{-1}f−1 is defined by

f−1(x)=1x−2,x∈R,x≠0 f^{-1}(x) = \frac{1}{x} - 2, \quad x \in \mathbb{R}, x \neq 0 f−1(x)=x1​−2,x∈R,x=0
a.

Write down the range of f−1(x)f^{-1}(x)f−1(x)

[2]
b.

Find an expression for f(x)f(x)f(x) and state its domain

[3]
c.

g(x)=x2−3,x∈Rg(x) = x^2 - 3, \quad x \in \mathbb{R}g(x)=x2−3,x∈R

Solve f−1g(x)=−32\displaystyle f^{-1}g(x) = -\frac{3}{2}f−1g(x)=−23​

[3]
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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