(a)[3]
Find a formula for $f^{-1}(x)$.
(b)[4]
Show that $1 - \frac{8}{x^2 + 4}$ may be rewritten as $\frac{x^2 - 4}{x^2 + 4}$ and hence state the range of $f$.
(c)[1]
Explain why the composite function $ff$ is not defined.
Mathematics 9709 · AS & A Level · Functions
Functions — practice question
The function $f$ is given by $f(x) = \dfrac{x^2 - 4}{x^2 + 4}$, with the condition $x > 2$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Removing the denominator and rearranging to make $x^2$ the subject.” …
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