Mathematics 0580 · IGCSE · Functions

Functions — practice question

The functions are $f(x)=1-3x$, $g(x)=(x-1)^2$ and $h(x)=\frac{3}{x}, x \ne 0$.
(a)[1]

Find the value of $g(3)$.

(b)[2]

Find $f(-2)$ and give your answer in its simplest form.

(c)[2]

Find the inverse function, $f^{-1}(x)$.

(d)[5]

Since $gf(x)-g(x)f(x)=3x^3+ax^2+bx+c$, find the value of each of $a$, $b$ and $c$.

(e)[3]

Find $h(x)-f(x)$, and present your answer as a single fraction in simplest form.

(f)[1]

Given $h(x^n)=3x^7$, find the value of $n$.

Worked solution & mark scheme

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