CBSE 2024 · Region 3 · Set 3 · Q33 · 5 marks
Let $\displaystyle \mathrm{A}=\mathrm{R}-\{3\}$ and $\displaystyle \mathrm{B}=\mathrm{R}-\{\mathrm{a}\}$. Find the value of 'a' such that the function $\displaystyle \mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ defined by $\displaystyle \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}-2}{\mathrm{x}-3}$ is onto. Also, check whether the given function is one-one or not.
Marking-scheme solution
For onto, let $\displaystyle \mathrm{f}(\mathrm{x})=\mathrm{y}$\frac{\mathrm{x}-2}{\mathrm{x}-3}=\mathrm{y} \Rightarrow \mathrm{x}-2=\mathrm{x} \mathrm{y}-3 \mathrm{y}
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CBSE Class 12 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.