List of top Mathematics Questions on Functions asked in JEE Main

Let $N$ be the set of natural numbers and two functions $f$ and $g$ be defined as $f,g : N \to N$ such that : $f(n) = \begin{cases} \frac{n+1}{2} & \quad \text{if } n \text{ is odd}\\ \frac{n}{2} & \quad \text{if } n \text{ is even} \end{cases}$ and $g(n) = n-(-1)^n$. The $fog$ is :

Let N denote the set of all natural numbers. Define two binary relations on N as $R_1 = \{(x, y) \epsilon N \times N : 2x + y = 10 \}$ and $R_2 = \{(x, y) \epsilon N \times N : x + 2y = 10 \}$. Then :

For $x \, \in \, R , x \neq 0, x \neq 1,$ let $f_0(x) = \frac{1}{1-x}$ and $f_{n+1} (x) | = f_0 (f_n(x)), n = 0 , 1 , 2 , ...$ Then the value of $f_{100}(3) + f_1 \left(\frac{2}{3} \right) + f_2 \left( \frac{3}{2} \right)$ is equal to :

Let $R=\left\{ \left(3,3\right) \left(5,5\right), \left(9,9\right), \left(12,12\right), \left(5,12\right), \left(3,9\right), \left(3,12\right), \left(3,5\right)\right\}$ be a relation on the set $A=\left\{3,5,9,12\right\}$. Then, $R$ is:

If $4^{{\log }_{10}[x+1]}-6^{{\log }_{10}x}-2\cdot 3^{{\log }_{10}[x^2+2]}=0$ then the value of $\frac{1}{20x}$ is

Find the domain for function $$f(x)=[\sin x]\cos \left(\frac{\pi }{[x-1]}\right)$$

If the function $f(x)=x^3+e^{x/2}$ and $g(x)=f^{-1}$, then the value of $g^{\text{'}}(1)$ is

If f(x) = 3ax³ + bx² + cx + 1 and f(1) = 41, f'(1) = 2 and f''(2)= 4, then find (a² + b² + c²).