UniGeniusGCSE Maths · Edexcel 1MA1

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Formal, inverse and composite functions

3 exam-style questions. Answers and the mark for each step are on the last page.

  1. Question 1Non-calculator · 5 marks

    f(x)=3x−5f(x) = 3x - 5 and g(x)=x2g(x) = x^2.

    (a) Find f(4)f(4). (1)

    (b) Find fg(2)fg(2). (2)

    (c) Find f−1(x)f^{-1}(x). (2)

  2. Question 2Non-calculator · 5 marks

    f(x)=3x−5f(x)=3x-5 and g(x)=x2+1g(x)=x^2+1.

    (a) Find an expression for f−1(x)f^{-1}(x). (2)

    (b) Find all x satisfying f(g(x)) = f(10). (3)

  3. Question 3Non-calculator · 4 marks

    f(x)=5−2xf(x) = 5 - 2x.

    (a) Find the value of aa for which f(a)=f−1(a)f(a) = f^{-1}(a). (4)

Answers and marks

Question 1

(a) 77

  • B1 The correct answer, 77.

(b) 77

  • M1 Working out g(2)=4g(2) = 4 first.
  • A1 The correct answer, 77.

(c) f−1(x)=x+53f^{-1}(x) = \dfrac{x + 5}{3}

  • M1 Rearranging y=3x−5y = 3x - 5 to x=y+53x = \frac{y + 5}{3} (or reversing the operations).
  • A1 x+53\frac{x + 5}{3}.

Question 2

(a) x+53\frac{x+5}{3}

  • M1 Reverse subtraction, then multiplication.
  • A1 Correct answer: x+53\frac{x+5}{3}

(b) −3,3-3,3

  • M1 The one-to-one linear function can be undone on both sides.
  • M1 Keep both square roots.
  • A1 Correct answer: −3,3-3,3

Question 3

(a) a=53a = \frac{5}{3}

  • P1 Finding f−1(x)=5−x2f^{-1}(x) = \frac{5 - x}{2}.
  • P1 Forming 5−2a=5−a25 - 2a = \frac{5 - a}{2}.
  • P1 Clearing the fraction and collecting: 3a=53a = 5.
  • A1 a=53a = \frac{5}{3}.

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Formal, inverse and composite functions

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