List of top Mathematics Questions on Functions asked in CBSE CLASS XII

Find the domain of $p(x)=\sin^{-1}(1-2x^2)$. Hence, find the value of $x$ for which $p(x)=\frac{\pi}{6}$. Also, write the range of $2p(x)+\frac{\pi}{2}$.

Assertion : Let $ Z $ be the set of integers. A function $ f : Z \to Z $ defined as $ f(x) = 3x - 5 $, $ \forall x \in Z $, is a bijective.
Reason (R): A function is bijective if it is both surjective and injective.

If $f : \mathbb{N} \rightarrow \mathbb{W}$ is defined as \[ f(n) = \begin{cases} \frac{n}{2}, & \text{if } n \text{ is even} \\ 0, & \text{if } n \text{ is odd} \end{cases} \] then $f$ is :

Assertion (A):
$ f(x) = \begin{cases} 3x - 8, & x \leq 5 \\ 2k, & x > 5 \end{cases} $
is continuous at $ x = 5 $ for $ k = \frac{5}{2} $.

Reason (R):
For a function $ f $ to be continuous at $ x = a $,
\[ \lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x) = f(a) \]

The absolute maximum value of function $ f(x) = x^3 - 3x + 2 $ in $ [0, 2] $ is:

For real $x$, let $f(x) = x^3 + 5x + 1$. Then :

Let A be the set of 30 students of class XII in a school. Let f : A -> N, N is a set of natural numbers such that function f(x) = Roll Number of student x.
On the basis of the given information, answer the followingIs $ f $ a bijective function?

Find $ k $ so that the function \[ f(x) = \begin{cases} \frac{x^2 - 2x - 3}{x + 1} & \text{if } x \neq -1 \\ k & \text{if } x = -1 \end{cases} \] is continuous at $ x = -1 $.

Domain of $ \sin^{-1}(2x^2 - 3) $ is:

Let $A = \{1, 2, 3\}$ and $B = \{4, 5, 6\}$. A relation $R$ from $A$ to $B$ is defined as $R = \{(x, y) : x + y = 6, x \in A, y \in B \}$. (i) Write all elements of $R$.
(ii) Is $R$ a function? Justify.
(iii) Determine domain and range of $R$.

Let $ \mathbb{Z} $ denote the set of integers. Then, the function $ f : \mathbb{Z} \to \mathbb{Z} $ defined as $ f(x) = x^3 - 1 $ is:

The greatest integer function defined by $ f(x) = [x] $, $ 1 < x < 3 $ is not differentiable at $ x = $:

For the function $ f(x) = x^3 $, $ x = 0 $ is a point of:

If $A = \begin{bmatrix} 1 & -2 & 0 \\ 2 & -1 & -1 \\ 0 & -2 & 1 \end{bmatrix}$, find $A^{-1}$ and use it to solve the following system of equations: \[ x - 2y = 10, \quad 2x - y - z = 8, \quad -2y + z = 7. \]

Find: \[ \int_{\pi/6}^{\pi/3} \frac{\sin x + \cos x}{\sqrt{\sin 2x}} \, dx. \]

A relation $ R $ defined on set $ A = \{x : x \in \mathbb{Z} \text{ and } 0 \leq x \leq 10\} $ as $ R = \{(x, y) : x = y$ is given to be an equivalence relation. The number of equivalence classes is:

$ \int_a^b f(x) \, dx $ is equal to: