IGCSE Mathematics (0580)

Functions

What this topic tests, the mistakes that cost marks, and one exam-style question worked through step by step.

Key ideas and common mistakes

Solving exponential equations with the same base requires expressing both sides as powers of that base, including using negative exponents for reciprocals.
Common mistake: Students often miss that 1/81 = 3^(-4), not 3⁴.
Correctly apply the order of operations by multiplying before subtracting when evaluating an expression like f(x) = a - bx at a given value, rather than subtracting first then multiplying.
To find the inverse of a linear function, reverse the order of operations: undo addition/subtraction before multiplication/division.
Common mistake: A common mistake is to divide before subtracting, which gives the wrong inverse.
Evaluating a composite function like gg(x) means applying g to the result of g(x), not multiplying or squaring g(x).
Common mistake: The trap is to confuse gg(x) with [g(x)]² or g(x) × g(x).
Solving an equation involving the inverse of a function requires reversing the mapping: set the original function equal to the given value and solve for the input, not the output.
When solving f(x) = g(x) for linear functions, collect all x terms on one side and all constants on the other, being careful to change the sign when moving terms across the equals sign.
Common mistake: Forgetting this leads to incorrect cancellation or sign errors.

Find the value of x when j(x) = 1/81.

Try it first, then show the working

Answer: -4

20 exam-style questions on Functions, each marked to the scheme.