List of top Mathematics Questions on Relations and functions asked in GUJCET

The maximum value of the function \( f(x) = -|x+1| + 3, \; x \in \mathbb{R} \) is _____

If function \( f \) is continuous at point \( x = \pi \) and \[ f(x) = \begin{cases} kx + 1, & x \le \pi \\ \cos x, & x>\pi \end{cases} \] then the value of \( k \) is ______

Let \( f : \mathbb{N} \rightarrow \mathbb{N} \) be defined by \[ f(n) = \begin{cases} \frac{n+1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases} \] for all \( n \in \mathbb{N} \). Then \( f \) is _____

Let \( R \) be the relation in the set \( \mathbb{N} \) given by \( R = \{(a,b) : a = b - 2, \; b<6\} \), then _____