List of top Mathematics Questions on Functions asked in VITEEE

Let \( f: \mathbb{R} \to \mathbb{R}, g: \mathbb{R} \to \mathbb{R} \) be two functions such that \[ f(x) = 2x - 3, \quad g(x) = x^3 + 5. \] \text{The function} \( (f \circ g)^{-1}(x) \) is equal to:

The domain of the function \[ f(x) = \sqrt{\frac{1}{|x-2| - (x-2)}} \] \text{is:}

The range of the function \[ f(x) = \frac{1}{2 - \cos 3x} \] is

The domain and range of the function \( f(x) = 2 - |x - 5| \) is

The number of surjective functions from \( A \) to \( B \) where \( A = \{1,2,3,4\} \) and \( B = \{a, b\} \) is

If \( f(x) = (1 + x)^2 \) for \( x>0 \), then \( f(x) \) is

If \( e^x = y + \sqrt{1 + y^2} \), then the value of \( y \) is

The domain of the function \[ f(x) = \frac{1}{\log(1 - x)} + \sqrt{x + 2} \] is

The domain of the function \[ f(x) = \frac{\sqrt{4 - x^2}}{\sin^{-1}(2 - x)} \] is:

Let \( R: \mathbb{R} \to \mathbb{R} \) be defined as \( f(x) = x^2 + 1 \), find \( f^{-1}(-5) \):

If D is the set of all real x such that \( 1 - e^{(1/x)} \) is positive, then D is equal to:

If $D$ is the set of all real $x$ such that $1-e^{\left(1/ x\right)-1}$ is positive, then $D$ is equal to

If \(f(x)=\sqrt{\log_{10}(x^2)}\), the set of all values of \(x\) for which \(f(x)\) is real, is

Domain of the function \(f(x)=\log_x(\cos x)\), is

Range of the function \(y=\sin^{-1}\left(\dfrac{x^2}{1+x^2}\right)\), is

Let \(S\) be a set containing \(n\) elements. Then, number of binary operation on \(S\) is

The number of solutions of the equation \(\sin(e^x)=5+x-5^x\), is

Let $S$ be a set containing $n$ elements. Then, number of binary operations on $S$ is

If \(f:[2,3]\rightarrow \mathbb{R}\) is defined by \(f(x)=x^3+3x-2\), then the range \(f(x)\) is contained in the interval

Let \(S\) be a finite set containing \(n\) elements. Then the total number of commutative binary operation on \(S\) is

Let P, Q, R and S be statements and suppose that \(P\to Q \to R \to P\); if \(\sim S \to R\), then

Let \([\,]\) denote the greatest integer function and \(f(x)=[\tan^2 x]\). Then

If $R$ be a relation defined as $aRb iff |a - b| > 0$, then the relation is

The number of real roots of the equation \[ \left( x + \frac{1}{x} \right)^3 + \frac{1}{x} = 0 \] is

Let \( A = \{ 1, 2, 3, \dots, n \} \) and \( B = \{ a, b, c, \dots \} \), then the number of functions from A to B that are onto is