Cambridge IGCSE · International Mathematics (0607)

Functions: Practice Questions

1 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Functions.

6 questions20 marksFree, no account

Question 1

1 mark

Given the functions \(f(x) = 2x - 1\) and \(g(x) = x^2 + 3\), find the value of the composite function \(gf(2)\).

Question 2

3 marks

Find the inverse function, \(f^{-1}(x)\), for \(f(x) = x + 4\).

Write your answer out first, then check it against the worked solution.

Question 3

4 marks

Find the coordinates of the vertex of the quadratic function \(f(x) = x^2 - 6x + 5\).

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Question 4

4 marks

A quadratic function \(f(x)\) has a vertex at \((3, -1)\) and passes through the point \((1, 7)\). Find the value of the stretch factor \(a\) when the function is written in the form \(f(x) = a(x - h)^2 + k\).

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Question 5

3 marks

Consider the functions \( f(x) = 4x - 5 \) and \( g(x) = 3(x + 2) \).

(a) Calculate the value of \( f(6) \).
(b) Find the value of \( x \) when \( g(x) = 27 \).
(c) Work out the value of \( f(2) + g(1) \).

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Question 6

5 marks

Consider the functions \( f(x) = \frac{2x - 3}{5} \) and \( g(x) = x^2 + 1 \).

(a) Calculate the value of \( f(9) \).
(b) Find the inverse function \( f^{-1}(x) \).
(c) Find the composite function \( g(f(x)) \). Give your answer in the form \( \frac{ax^2 + bx + c}{25} \).

Write your answer out first, then check it against the worked solution.

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