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5 marksFunctions

CAPE Pure Mathematics Unit 1 · May/June 2023 · Paper 2 · Question 2(a)

Let f(x) = 7x + 2. Prove that f is bijective.

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  1. 2(b)The roots of the cubic equation 3x^3 - x^2 - 2x + 1 = 0 are \alpha, \beta and \gamma. Determine the equation whose roots are 1/\alpha, 1/\beta and 1/\gamma.[8 marks]
  2. 2(c)(i)On the axes provided, sketch and label the graph of g(x) = |x^2 + 6x + 8|.[3 marks]
  3. 2(c)(ii)On the same axes, sketch and label the inverse of f for x \ge -3.[5 marks]
  4. 2(d)Given that g(x) = (2x + 3)/(x + 3), prove that g^{-1}(2) does not exist.[4 marks]

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