Inverse and Composite Functions worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 36 marks Sheet 1

4 marks
\(f(x) = 2x - 3\) and \(g(x) = 4x - 7\)

(a)
Find the value of \(fg(2)\).

(b)
Find the value of \(gf(2)\).
3 marks
\(f(x) = ax - 5\)

\(f(3) = 13\)

Work out the value of \(a\).
3 marks
\(f(x) = 7x + 5\) and \(g(x) = 6x - 5\)

Find \(fg(x)\).

Give your answer in the form \(px + q\), where \(p\) and \(q\) are integers.
3 marks
\(f(x) = 6x - 6\)

Find an expression for \(f^{-1}(x)\).
3 marks
\(f(x) = 7x - 6\) and \(g(x) = x + 4\)

\(fg(k) = 50\)

Find the value of \(k\).
4 marks
\(f(x) = 5x + 6\)

(a)
Work out \(f^{-1}(x)\).

(b)
Solve the equation \(f^{-1}(x) = -3\).
5 marks
\(f(x) = x^2 - 1\) and \(g(x) = x - 3\)

(a)
Work out \(gf(x)\).

(b)
Work out \(fg(x)\).

Give your answer in the form \(x^2 + px + q\).
4 marks
\(f(x) = x^2\) and \(g(x) = 4x + 12\)

Solve \(f(x) = g(x)\).
4 marks
\(f(x) = 6x + 4\) and \(g(x) = 2x + 8\)

(a)
Work out \(fg(-3)\).

(b)
Work out \(gf(-3)\).
3 marks
\(f(x) = ax + 2\)

\(f(2) = 8\)

Find the value of \(a\).

Answers