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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 6 · Set 1 · Q23
Determine the values of x for which f ( x )=(x -4)/(x +1), x ≠-1 is an increasing or a decreasing function.
Determine the values of x for which $\displaystyle \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}-4}{\mathrm{x}+1}, \mathrm{x} \neq-1$ is an increasing or a decreasing function.
Marking-scheme solution
\[\mathrm{f}^{\prime}(\mathrm{x})=\frac{\mathrm{x}+1-\mathrm{x}+4}{(\mathrm{x}+1)^{2}}=\frac{5}{(\mathrm{x}+1)^{2}}>0
\]
Hence f is increasing in its domain.
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.