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4 marksFunctions

CAPE Pure Mathematics Unit 1 · May/June 2026 · Paper 2 · Question 2(c)(i)

The function f is defined by f(x) = (5x + 1)/(x - 2), where x ∈ ℝ, x ≠ 2.

Determine whether f is injective.

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Other parts of this question

  1. 2(a)(i)Complete the table of values for h(x) = 5 - 2^(x+1) for x = 0, 1, 2, 3, 4.[2 marks]
  2. 2(a)(ii)On the grid provided on page 9, plot the graph of h(x) = 5 - 2^(x+1).[2 marks]
  3. 2(b)(i)On the grid provided on page 10, sketch the graph of y = |f(x)|.[2 marks]
  4. 2(b)(ii)On the grid provided on page 10, sketch the graph of y = |g(x)|.[2 marks]
  5. 2(c)(ii)Assuming that f is a bijective function, determine an expression for f⁻¹(x).[5 marks]
  6. 2(d)(i)Solve for x: 3^(4x + 1) = 177 147.[3 marks]
  7. 2(d)(ii)Solve for x: log₂(x + 6) + log₂(x + 2) = 5.[5 marks]

More practice: the rest of this paper · more Functions questions · all CAPE Pure Mathematics Unit 1 past papers