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Functions and Graphs

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Question 181

The function fff is defined by

f(x)=∣x−12∣+15 for x∈R f(x) = |x - 12| + 15 \text{ for } x \in \mathbb{R} f(x)=∣x−12∣+15 for x∈R

The function ggg is defined by

g(x)=e2x+15 g(x) = e^{2x} + 15 g(x)=e2x+15

where ggg has its greatest possible domain.

a.

Using set notation, state the range of fff.

[1]
b.

State the domain of ggg.

[1]
c.

The composite function hhh is given by

h(x)=fg(x) for x∈domain of g h(x) = f g(x) \text{ for } x \in \text{domain of } g h(x)=fg(x) for x∈domain of g

(i) Write down an expression for h(x)h(x)h(x) in terms of xxx. (ii) Determine if hhh has an inverse. Fully justify your answer.

[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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