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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 5 · Set 1 · Q23
Determine the values of x for which f ( x )=(x -3)/(x +1), x ≠-1 is an increasing function.
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 $\displaystyle x \in \mathbb{R}-\{-1\}$
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