Inverse Function and Fixed Point

00:00 6 marks

Let $f(x) = \frac{2x – 1}{x + 3}$ for $x
eq -3$.
(a) Find an expression for $f^{-1}(x)$. [3]
(b) Find the value of $a$ such that $f(a) = f^{-1}(a)$. [3]

Hint Hint

Hint

For part (a), set $y = f(x)$ and solve the equation for $x$ in terms of $y$, then interchange $x$ and $y$. For part (b), equate $f(a)$ and $f^{-1}(a)$ and solve the resulting equation.

Answer Answer
Explanation Explanation
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Answer Answer

Complete Answer

f⁻¹(x) = (3x + 1)/(2 – x) and there is no real value of a for which f(a) = f⁻¹(a) (since the resulting quadratic has no real solutions).

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