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3.1 Algebra and functions (A-level only)

3.1 Algebra and functions (A-level only)

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Question 36

The functions f f\,f and g g\,g are defined by

f:x→ln⁡(5x−2),x∈R,x>25 f: x \rightarrow \ln(5x - 2), \quad x \in \mathbb{R}, x > \frac{2}{5} f:x→ln(5x−2),x∈R,x>52​ g:x→2x−4,x∈R,x≠4 g: x \rightarrow \frac{2}{x-4}, \quad x \in \mathbb{R}, x \neq 4 g:x→x−42​,x∈R,x=4
a.

Find the exact value of fg(6)fg(6)fg(6)

[2]
b.

Find an expression for f−1(x)f^{-1}(x)f−1(x) and state its domain

[4]
c.

Sketch the graphs of f(x)f(x)f(x) and f−1(x)f^{-1}(x)f−1(x) on the same diagram

[3]
d.

Sketch the graph of y=∣g(x)∣y = |g(x)|y=∣g(x)∣

[3]
e.

Find the exact values of ∣2x−4∣=4\displaystyle | \frac{2}{x-4} | = 4∣x−42​∣=4

[3]
Markscheme

3.1 Algebra and functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.1 Algebra and functions (A-level only)

281 exam-style questions on CCEA A Level Maths 3.1 Algebra and functions (A-level only), covering 3.1.1 Algebra and functions (A-level only), 3.1.2 Algebra and functions (A-level only), 3.1.3 Algebra and functions (A-level only), 3.1.4 Algebra and functions (A-level only), 3.1.5 Algebra and functions (A-level only), 3.1.6 Algebra and functions (A-level only), 3.1.7 Algebra and functions (A-level only), 3.1.8 Algebra and functions (A-level only), 3.1.9 Algebra and functions (A-level only), and 3.1 Algebra and functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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