Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The function $f$ is given by $f(x) = \frac{2x + 1}{2x - 1}$, with the condition $x < \frac{1}{2}$.
(a(i))[1]

State the numerical value of $f(-1)$.

(a(ii))[2]

The diagram displays the graph of $y = f(x)$. On this diagram, sketch $y = f^{-1}(x)$. Include any mirror line that is needed.

(a(iii))[4]

Find an expression for $f^{-1}(x)$, and state the domain of $f^{-1}$.

(b)[3]

The function $g$ is defined by $g(x) = 3x + 2$ for $x \in \mathbb{R}$. Solve the equation $f(x) = g f\left(\frac{1}{4}\right)$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: So $f(-1)=\frac{1}{3}$.

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