List of top Mathematics Questions on types of functions asked in MET

Let \( f:\mathbb{N} \to \mathbb{N} \) be defined as \[ f(n)= \begin{cases} \frac{n+1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases} \] Then \( f \) is:
Let \( f(x) = \frac{1}{\sqrt{1 + x^2}} \), then:
If \( f(x) = \frac{a^x + a^{-x}}{2} \) and \( f(x+y) + f(x-y) = k f(x)f(y) \), then \( k \) is equal to
A man \(1.6\mathrm{m}\) high walks at the rate of \(30\mathrm{m/min}\) away from a lamp which is \(4\mathrm{m}\) above ground. How fast is the man's shadow lengthening?
The function \( f(x) = \max\left\{(1 - x), (1 + x), 2\right\}, \, x \in (-\infty, \infty) \) is equivalent to
If $f: R \to R$ is defined by $f(x) = 3x - 4$, then $f^{-1(x)$ is: