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

Let $A = \{x : x \in \mathbb{R}, \, x \text{ is not a positive integer}\}$. Define $f: A \to \mathbb{R}$ as $f(x) = \dfrac{2x}{x-1}$, then $f$ is:

Which of the following functions is not invertible?

Domain of the function \( f(x) = \frac{1{(x-2)(x-5)} \) is:}

On the set of integers $Z$. define $f: Z \to Z$ as $ f(n) = \begin{cases} n/2 & \quad \text{if } n \text{ is even}\\ 0 & \quad \text{if } n \text{ is odd}\\ \end{cases} $ then $'f'$ is

Let $(gof)(x) = sin x$ and $(fog)(x) = (sin \sqrt x)^2,$ Then

If \(f(x) = x e^{x(1-x)}\) then f(x) is