Mathematics 0580 · IGCSE · Functions

Functions — practice question

The functions are given by $f(x)=2x+5$, $g(x)=1-2x$, $h(x)=\frac{1}{x+1}$, $x\ne-1$, and $j(x)=2^x$.

(a)[1]

Find the value of $g(-3)$.

(b)[4]

Find $f(x)g(x)+fg(x)+1$. Write your answer in its simplest form.

(c)[2]

Find $g^{-1}(x)$.

(d)[2]

Find the value of $h(1)$.

(e)[3]

Simplify $\frac{1}{f(x)}-h(x)$. Give your answer as one fraction in its simplest form.

(f)[1]

Find the value of $x$ when $j(x)=\frac{1}{32}$.

(g)[1]

Find the value of $x$ when $j^{-1}(x)=0$.

Worked solution & mark scheme

This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct result is $7$.” …