CBSE 2026 · Region 5 · Set 1 · Q23 · 2 marks
Determine the values of x for which $\displaystyle \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}-3}{\mathrm{x}+1}, \mathrm{x} \neq-1$ is an increasing function.
Marking-scheme solution
$\displaystyle f^{\prime}(x)=\dfrac{(x+1) \cdot 1-(x-3) \cdot 1}{(x+1)^{2}}$
$\displaystyle =\dfrac{4}{(x+1)^{2}}>0$
$\displaystyle \therefore f(x)$ is an increasing function for all $\displaystyle x \in \mathbb{R}-\{-1\}$
Application of DerivativesIncreasing and Decreasing FunctionsApplyvery_short_answermedium
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CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.