Mathematics 0580 · IGCSE · Functions

Functions — practice question

With $f(x) = 7 - 3x$ and $g(x) = x^2 - 16$.
(a(i))[2]

Find the values of $x$ for which $g(x) = 20$.

(a(ii))[2]

Find the expression for $f^{-1}(x)$.

(a(iii))[3]

Find $gf(x) + 1$, and give your answer in simplest form.

(a(iv))[4]

On the axes, sketch the graph of $y = g(x)$. On your sketch, show where the graph meets the axes.

(a(v))[5]

Find the equation of the tangent to the graph of $y = g(x)$ at $x = -3$. Give your answer in the form $y = mx + c$.

(b(i))[2]

On the axes, sketch the curve for $y = h(x)$.

(b(ii))[1]

Write down the equation of the asymptote for the graph of $y = h(x)$.

Worked solution & mark scheme

This 19-mark question has a full step-by-step worked solution and mark scheme. One marking point: $x=6$ and $x=-6$

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