Functions and Graphs
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Question 87
The diagram shows a sketch of y=g(x)y = g(x)y=g(x), where
g(x)={3−2xx<1(x−1)2+1x≥1 g(x) = \begin{cases} 3 - 2x & x < 1 \\ (x - 1)^2 + 1 & x \geq 1 \end{cases} g(x)={3−2x(x−1)2+1x<1x≥1a.[2]
Find the value of gg(0)gg(0)gg(0)
b.[4]
Find all the values of x x\,x for which g(x)>5g(x) > 5g(x)>5
c.[1]
The function h h\,h is defined as h(x)=(x−1)2+1x≥1h(x) = (x - 1)^2 + 1 \quad x \geq 1h(x)=(x−1)2+1x≥1. Explain why h h\,h has an inverse but g g\,g does not.
d.[3]
Solve the equation h−1(x)=2h^{-1}(x) = 2h−1(x)=2
Functions and Graphs Questions
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.