Functions — IGCSE Mathematics - Additional (0606) questions by topic
Functions questions ask you to find the least value of a domain restriction so that an inverse function exists, rewrite a quadratic function in completed-square form with named constants, explain why a function can be composed with itself, and solve an equation formed by composing two given functions. Find, draw, determine and explain are the top command words, with explain tasks needing a reasoned justification about domain and range rather than just an answer.
Marks range from 4 to 12 across the 5 real questions gathered here, all from 2025 papers. Because composite and inverse function questions depend on domain restrictions holding at every step, submit your solutions for instant marking to check the restriction you stated is actually the one the function needs.
May–June 2025, Paper 12
It is given that f(x) = 2 ln(3x - 4), for x a, and that f^(-1) exists. Find the least possible value of a.
Answer this question and get it marked →May–June 2025, Paper 13
The function f is defined by f(x) = -2x^2 + 9x - 10 for 0 <= x <= 3. Write f(x) in the form a + b(x + c)^2 where a, b and c are constants.
Answer this question and get it marked →May–June 2025, Paper 22
Functions f and g are such that f(x) = 3x / (x + 4) for x 0 g(x) = sqrt(x + 2) for x -2. Solve the equation fg(x) = 1.
Answer this question and get it marked →May–June 2025, Paper 23
Variables x and y are such that when sqrt(y) is plotted against x^3 a straight line graph passing through the points (2, 5) and (10, 21) is obtained. Find y in terms of x.
Answer this question and get it marked →The function f is defined by f(x) = 2x − 1 for x ∈ ℝ. Explain why the function f^2 can be formed.
Answer this question and get it marked →