CBSE 2026 · Region 3 · Set 3 · Q33 · 5 marks

Show that a function $\displaystyle \mathrm{f}: \mathrm{R}_{+} \rightarrow \mathrm{A} \subset \mathrm{N}$, defined as $\displaystyle \mathrm{f}(\mathrm{x})=4 \mathrm{x}^{2}+12 \mathrm{x}+15$ is one-one. Find set A so that f is onto where $\displaystyle \mathrm{R}_{+}=[0, \infty)$. Also, find if there exists $\displaystyle \mathrm{a} \in \mathrm{R}_{+}$such that $\displaystyle \mathrm{f}(\mathrm{a})=7$. Justify.

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.