List of top Mathematics Questions on Types of Functions asked in CBSE Class XII

Check whether the function \[ f:\mathbb{R}\setminus\{3\}\rightarrow\mathbb{R} \] defined by \[ f(x)=\frac{x-2}{x-3} \] is onto (surjective) or not.

Show that $f : \mathbf{R}_+ \to [-5, \infty)$ given by $f(x) = 4x^2 + 4x - 5$ is both one-one and onto where $\mathbf{R}_+ = [0, \infty)$. Also, find $p \in \mathbf{R}_+$ such that $f(p) = 3$.

Check whether the function \( f : \mathbb{Z} \times \mathbb{Z} \rightarrow \mathbb{Z} \times \mathbb{Z} \) defined as \( f(x, y) = (2y, 3x) \) is injective (one-to-one) or not.