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Answer the following.
Let f: mathbbR - {-1/3} → mathbbR - {0} be defined as f(x) = 5/(3x + 1) is invertible. Find f⁻¹(x).
Let $f: \mathbb{R} - \left\{-\frac{1}{3}\right\} \to \mathbb{R} - \{0\}$ be defined as $f(x) = \frac{5}{3x + 1}$ is invertible. Find $f^{-1}(x)$.
Answer
Answer
Let $y = \frac{5}{3x+1}$.
$y(3x+1) = 5$
$3xy = 5 - y$
$x = \frac{5-y}{3y}$
Hence $f^{-1}(x) = \frac{5-x}{3x}$, $x \in \mathbb{R} - \{0\}$.
Final answer: $\frac{5-x}{3x}$