Relations and Functions Question - CBSE

Question

Let $f: \mathbb{R} - \{-4/3\} \rightarrow \mathbb{R} - \{4/3\}$ be defined as $f(x) = \dfrac{4x + 3}{3x + 4}$. Show that $f$ is bijective and find $f^{-1}$. Also evaluate $f^{-1}(0)$ and $f^{-1}(1)$.

Accepted Answer

One-one proof: $7x_1 = 7x_2 \Rightarrow x_1 = x_2$. [1.0 Mark]
Onto proof: $x = \dfrac{4y-3}{4-3y} \in \mathbb{R}-\{-4/3\} \Rightarrow f$ is bijective. [1.5 Marks]
Inverse $f^{-1}(x) = \dfrac{4x - 3}{4 - 3x}$. [1.5 Marks]
Evaluations: $f^{-1}(0) = -3/4$ and $f^{-1}(1) = 1$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Proving One-one: 1.0 Mark
Proving Onto: 1.5 Marks
Evaluating inverse function $f^{-1}(x) = (4x-3)/(4-3x)$: 1.5 Marks
Evaluating $f^{-1}(0) = -3/4$ and $f^{-1}(1) = 1$: 1.0 Mark

Question:

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