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1.2 Algebra and Functions

1.2 Algebra and Functions

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Question 253

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

1.2 Algebra and Functions Questions

  1. A Level
  2. /Maths
  3. /1.2 Algebra and Functions

566 exam-style questions on OCR A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Indices, 1.2.2 Surds, 1.2.3 Simultaneous equations, 1.2.4 Quadratic functions, 1.2.5 Completing the square, 1.2.6 Solving quadratic equations, 1.2.7 Inequalities, 1.2.8 Expressing solutions of inequalities, 1.2.9 Representing inequalities graphically, 1.2.10 Manipulating polynomials, 1.2.11 Simplifying rational expressions, 1.2.12 The modulus function (A-level only), 1.2.13 Graphs of functions, 1.2.14 Sketching curves from equations, 1.2.15 Sketching reciprocal curves, 1.2.16 Interpreting solutions graphically, 1.2.17 Intersection points of graphs, 1.2.18 Proportional relationships, 1.2.19 Graph of the modulus of a linear function (A-level only), 1.2.20 Solving modulus equations graphically (A-level only), 1.2.21 Definition of a function (A-level only), 1.2.22 Inverse and composite functions (A-level only), 1.2.23 Simple graph transformations, 1.2.24 Combinations of graph transformations (A-level only), 1.2.25 Partial fractions (A-level only), and 1.2.26 Models in context. Each one has a worked solution and a mark scheme showing where the marks go.

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