List of top Mathematics Questions on Functions asked in JEE Main

Let \( f : \mathbb{R} \to \mathbb{R} \) be defined as \( f(x) = 2x - 1 \) and \( g : \mathbb{R} \setminus \{1\} \to \mathbb{R} \) be defined as \( g(x) = \dfrac{x - \frac{1}{2}}{x - 1} \). Then the composition function \( f(g(x)) \) is :

Let $g: N \to N$ be defined as $g(3n+1) = 3n+2, g(3n+2) = 3n+3, g(3n+3) = 3n+1$, for all $n \ge 0$. Then which of the following statements is true ?

If a + α = 1, b + β = 2 and a f(x) + α f(1/x) = b x + β / x, then [f(x) + f(1/x)] / [x + 1/x] is ________

Let $f: R \rightarrow R$ be defined as, $f(x) = \begin{cases} -55x, & \text{if } x < -5 \\ 2x^3 -3x^2 -120x, & \text{if } 5 \le x \le 4 \\ 2x^3 -3x^2-36x-336& \text{if } x > 4, \end{cases} $ Let $A=\{ x \in R : f$ is increasing $\} .$ Then $A$ is equal to

The inverse function of $f\left(x\right) = \frac{8^{2x}-8^{-2x}}{8^{2x} + 8^{-2x}}, x\epsilon \left(-1, 1\right),$ is __________.

Let $f :(-1, \infty) \rightarrow R$ be defined by $f (0)=1$ and $f ( x )=\frac{1}{ x } \log _{ e }(1+ x ), x \neq 0 .$ Then the function $f$

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:

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

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