Functions – Algebra MCQs

By: Prof. Dr. Fazal Rehman Shamil | Last updated: January 31, 2025

\[
\textbf{MCQs on Functions in Algebra with Answers}
\]

\[
\textbf{Q1: Which of the following is the definition of a function?}
\]
\[
\text{(A) A relation where each input has exactly one output} \quad \text{(B) A relation where each input has multiple outputs} \quad \text{(C) A set of numbers} \quad \text{(D) A set of ordered pairs}
\]
\[
\textbf{Answer: (A) A relation where each input has exactly one output}
\]

\[
\textbf{Q2: What is the range of the function \( f(x) = x^2 + 3x + 2 \)?}
\]
\[
\text{(A) All real numbers} \quad \text{(B) \( x \geq 0 \)} \quad \text{(C) \( x \geq -2 \)} \quad \text{(D) \( y \geq 0 \)}
\]
\[
\textbf{Answer: (A) All real numbers}
\]

\[
\textbf{Q3: The function \( f(x) = 2x + 5 \) is an example of which type of function?}
\]
\[
\text{(A) Quadratic Function} \quad \text{(B) Linear Function} \quad \text{(C) Exponential Function} \quad \text{(D) Constant Function}
\]
\[
\textbf{Answer: (B) Linear Function}
\]

\[
\textbf{Q4: If \( f(x) = 3x – 4 \), what is \( f(2) \)?}
\]
\[
\text{(A) 4} \quad \text{(B) 6} \quad \text{(C) 2} \quad \text{(D) 8}
\]
\[
\textbf{Answer: (B) 6}
\]

\[
\textbf{Q5: What is the domain of the function \( f(x) = \frac{1}{x-2} \)?}
\]
\[
\text{(A) \( x \neq 0 \)} \quad \text{(B) \( x \neq 2 \)} \quad \text{(C) \( x \geq 0 \)} \quad \text{(D) All real numbers}
\]
\[
\textbf{Answer: (B) \( x \neq 2 \)}
\]

\[
\textbf{Q6: If \( f(x) = x^2 – 1 \), what is \( f(3) \)?}
\]
\[
\text{(A) 8} \quad \text{(B) 6} \quad \text{(C) 7} \quad \text{(D) 9}
\]
\[
\textbf{Answer: (A) 8}
\]

\[
\textbf{Q7: Which of the following is a one-to-one function?}
\]
\[
\text{(A) \( f(x) = x^2 \)} \quad \text{(B) \( f(x) = x^3 \)} \quad \text{(C) \( f(x) = x + 2 \)} \quad \text{(D) All of the above}
\]
\[
\textbf{Answer: (B) \( f(x) = x^3 \)}
\]

\[
\textbf{Q8: What is the inverse of the function \( f(x) = 2x + 3 \)?}
\]
\[
\text{(A) \( f^{-1}(x) = \frac{x-3}{2} \)} \quad \text{(B) \( f^{-1}(x) = \frac{x+3}{2} \)} \quad \text{(C) \( f^{-1}(x) = \frac{x}{2} – 3 \)} \quad \text{(D) \( f^{-1}(x) = x – 3 \)}
\]
\[
\textbf{Answer: (A) \( f^{-1}(x) = \frac{x-3}{2} \)}
\]

\[
\textbf{Q9: If \( f(x) = 3x + 4 \) and \( g(x) = 2x – 1 \), what is \( (f \circ g)(x) \)?}
\]
\[
\text{(A) \( 6x + 3 \)} \quad \text{(B) \( 6x + 3 \)} \quad \text{(C) \( 6x + 7 \)} \quad \text{(D) \( 5x + 5 \)}
\]
\[
\textbf{Answer: (A) \( 6x + 3 \)}
\]

\[
\textbf{Q10: What is the composition of functions \( f(x) = x+3 \) and \( g(x) = 2x \)?}
\]
\[
\text{(A) \( (f \circ g)(x) = 2x + 3 \)} \quad \text{(B) \( (f \circ g)(x) = x + 6 \)} \quad \text{(C) \( (f \circ g)(x) = 2x + 3 \)} \quad \text{(D) \( (f \circ g)(x) = 2x + 6 \)}
\]
\[
\textbf{Answer: (A) \( (f \circ g)(x) = 2x + 3 \)}
\]

More MCQs on Algebra (Collected from Past Papers)

  1. Elementary Algebra – MCQs
  2. Algebraic Expressions – MCQs
  3. Algebraic Identities – MCQs
  4. Commutative Algebra – MCQs
  5. Linear Equations – MCQs
  6. Graphing Linear Equations – MCQs
  7. Inequalities in Algebra – MCQs
  8. Absolute Value Inequalities – MCQs
  9. Exponent – MCQs
  10. Exponential Functions – MCQs
  11. Logarithms – MCQs
  12. Polynomials – MCQs
  13. Factoring Methods – MCQs
  14. Polynomial Arithmetic – MCQs
  15. Quadratic Equation – MCQs
  16. Linear Algebra – MCQs
  17. Matrices in Algebra – MCQs
  18. Functions in Algebra – MCQs
  19. Sequences in Algebra – MCQs
  20. Arithmetic in Algebra – MCQs
  21. Combining Like Terms in Algebra – MCQs
  22. Abstract Algebra – MCQs
  23. Sets in Algebra – MCQs
  24. Algebra Calculator – MCQs

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