VITEEE PYQs for Functions with Solutions: Practice VITEEE Previous Year Questions

Updated 3+ months ago

Functions is an important topic in the Mathematics section in VITEEE exam. Practising this topic will increase your score overall and make your conceptual grip on VITEEE exam stronger.

This article gives you a full set of VITEEE PYQs for Functions with explanations for effective preparation. Practice of VITEEE Mathematics PYQs including Functions questions regularly will improve accuracy, speed, and confidence in the VITEEE 2026 exam.

VITEEE PYQs for Functions with Solutions

1.
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
- $(-\infty, 1]$
- $\left(-\infty , 0\right)$
- $\left(1, \infty\right)$
- $\left(-\infty , 0\right)\cup\left(1, \infty\right)$
View Solution
2.
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:
- $ \left( \frac{x + 7}{2} \right)^{1/3} $
- $ \left( \frac{x - 7}{2} \right)^{1/3} $
- $ \left( \frac{x - 2}{7} \right)^{1/3} $
- $ \left( \frac{x + 7}{7} \right)^{1/3} $
View Solution
3.
If $f(x)=\sqrt{\log_{10}(x^2)}$, the set of all values of $x$ for which $f(x)$ is real, is
- $[-1,1]$
- $[1,\infty)$
- $(-\infty,-1]$
- $(-\infty,-1]\cup[1,\infty)$
View Solution
4.
The domain of the function \[ f(x) = \frac{\sqrt{4 - x^2}}{\sin^{-1}(2 - x)} \] is:
- $ [0, 2] $
- $ (0, 2) $
- $ [1, 2] $
- $ [1, 2] $
View Solution
5.
The domain and range of the function $ f(x) = 2 - |x - 5| $ is
- Domain = $ \mathbb{R}^*, $ Range = $ (-\infty, 1] $
- Domain = $ \mathbb{R}, $ Range = $ (-\infty, 2] $
- Domain = $ \mathbb{R}, $ Range = $ [0, 2] $
- Domain = $ \mathbb{R}, $ Range = $ (-\infty, 0] $
View Solution
6.
Range of the function $y=\sin^{-1}\left(\dfrac{x^2}{1+x^2}\right)$, is
- $\left(0,\frac{\pi}{2}\right)$
- $\left[0,\frac{\pi}{2}\right)$
- $\left(0,\frac{\pi}{2}\right]$
- $\left[0,\frac{\pi}{2}\right]$
View Solution
7.
The domain of the function \[ f(x) = \frac{1}{\log(1 - x)} + \sqrt{x + 2} \] is
- $ [-3, -2] \cup [0, \infty) $
- $ [-3, 2] $
- $ [0, \infty) $
- $ [-3, -2] \cup [2, \infty) $
View Solution
8.
The domain of the function \[ f(x) = \sqrt{\frac{1}{|x-2| - (x-2)}} \] \text{is:}
- $ (-\infty, 2] $
- $ (2, \infty) $
- $ (-\infty, 2) $
- $ [2, \infty) $
View Solution
9.
If D is the set of all real x such that $ 1 - e^{(1/x)} $ is positive, then D is equal to:
- $ (-\infty, -1] $
- $ (-\infty, 0) $
- $ (1, \infty) $
- $ (-\infty, 0) \cup (1, \infty) $
View Solution
10.
The range of the function \[ f(x) = \frac{1}{2 - \cos 3x} \] is
- (-2, ∞)
- [-3, 3]
- [1, 2]
- [1, ∞)
View Solution
11.
If $ e^x = y + \sqrt{1 + y^2} $, then the value of $ y $ is
- $ \frac{1}{2} (e^x - e^{-x}) $
- $ \frac{1}{2} (e^x + e^{-x}) $
- $ e^x $
- $ e^x + 2 $
View Solution
12.
If $ f(x) = (1 + x)^2 $ for $ x>0 $, then $ f(x) $ is
- continuous only at $ x = 0 $
- right continuous only at $ x = 0 $
- continuous at $ x = 0 $
- discontinuous at $ x = 0 $
View Solution
13.
The number of surjective functions from $ A $ to $ B $ where $ A = \{1,2,3,4\} $ and $ B = \{a, b\} $ is
- 14
- 12
- 16
- 15
View Solution
14.
Domain of the function $f(x)=\log_x(\cos x)$, is
- $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)-\{1\}$
- $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]-\{1\}$
- $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$
- None of these
View Solution
15.
Let $ R: \mathbb{R} \to \mathbb{R} $ be defined as $ f(x) = x^2 + 1 $, find $ f^{-1}(-5) $:
- $ \emptyset $
- $ \{ -5 \} $
- $ \{ 5 \} $
- $ \{ -5, 5 \} $
View Solution

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VITEEE PYQs for Functions with Solutions: Practice VITEEE Previous Year Questions

VITEEE PYQs for Functions with Solutions

1.
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

2.
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:

3.
If \(f(x)=\sqrt{\log_{10}(x^2)}\), the set of all values of \(x\) for which \(f(x)\) is real, is

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

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

6.
Range of the function \(y=\sin^{-1}\left(\dfrac{x^2}{1+x^2}\right)\), is

7.
The domain of the function \[ f(x) = \frac{1}{\log(1 - x)} + \sqrt{x + 2} \] is

8.
The domain of the function \[ f(x) = \sqrt{\frac{1}{|x-2| - (x-2)}} \] \text{is:}

9.
If D is the set of all real x such that \( 1 - e^{(1/x)} \) is positive, then D is equal to:

10.
The range of the function \[ f(x) = \frac{1}{2 - \cos 3x} \] is

11.
If \( e^x = y + \sqrt{1 + y^2} \), then the value of \( y \) is

12.
If \( f(x) = (1 + x)^2 \) for \( x>0 \), then \( f(x) \) is

13.
The number of surjective functions from \( A \) to \( B \) where \( A = \{1,2,3,4\} \) and \( B = \{a, b\} \) is

14.
Domain of the function \(f(x)=\log_x(\cos x)\), is

15.
Let \( R: \mathbb{R} \to \mathbb{R} \) be defined as \( f(x) = x^2 + 1 \), find \( f^{-1}(-5) \):

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VITEEE PYQs for Functions with Solutions

1.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

2.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:

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

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

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

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

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

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

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

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

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

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

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

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

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

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1.
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

2.
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:

3.
If \(f(x)=\sqrt{\log_{10}(x^2)}\), the set of all values of \(x\) for which \(f(x)\) is real, is

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

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

6.
Range of the function \(y=\sin^{-1}\left(\dfrac{x^2}{1+x^2}\right)\), is

7.
The domain of the function \[ f(x) = \frac{1}{\log(1 - x)} + \sqrt{x + 2} \] is

8.
The domain of the function \[ f(x) = \sqrt{\frac{1}{|x-2| - (x-2)}} \] \text{is:}

9.
If D is the set of all real x such that \( 1 - e^{(1/x)} \) is positive, then D is equal to:

10.
The range of the function \[ f(x) = \frac{1}{2 - \cos 3x} \] is

11.
If \( e^x = y + \sqrt{1 + y^2} \), then the value of \( y \) is

12.
If \( f(x) = (1 + x)^2 \) for \( x>0 \), then \( f(x) \) is

13.
The number of surjective functions from \( A \) to \( B \) where \( A = \{1,2,3,4\} \) and \( B = \{a, b\} \) is

14.
Domain of the function \(f(x)=\log_x(\cos x)\), is

15.
Let \( R: \mathbb{R} \to \mathbb{R} \) be defined as \( f(x) = x^2 + 1 \), find \( f^{-1}(-5) \):