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6 marksDeriving Inverse Functions

CSEC Mathematics · January 2011 · Paper 2 · Question 9(a)(ii)a)

Functions f(x) and g(x) are defined as: f(x) = (2x - 7)/x and g(x) = √(x + 3).

Write an expression in x for f⁻¹(x).

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Other parts of this question

  1. 9(a)(i)Evaluate f(5).[1 mark]
  2. 9(a)(ii)b)Write an expression in x for gf(x).[1 mark]
  3. 9(b)(i)Express the quadratic function 1 - 6x - x² in the form k - a(x + h)², where a, h and k are constants.[3 marks]
  4. 9(b)(ii)a)Hence state the maximum value of 1 - 6x - x².[2 marks]
  5. 9(b)(ii)b)Hence state the equation of the axis of symmetry of the quadratic function.[1 mark]
  6. 9(b)(iii)Determine the roots of 1 - 6x - x² = 0, giving your answers to 2 decimal places.[3 marks]

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