Sets, Relations and FunctionsPYQ May 25Question 4034 of 145
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The range of the function f(x)=3x−2\displaystyle f(x) = 3x - 2 is

Options

A(−∞,∞)\displaystyle (-\infty, \infty)
BR−{3}\displaystyle \mathbb{R} - \{3\}
C(−∞,0)\displaystyle (-\infty, 0)
D(0,−∞)\displaystyle (0, -\infty)
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Correct Answer

✅ Option a — (−∞,∞)\displaystyle (-\infty, \infty)

All Options:

  • A(−∞,∞)\displaystyle (-\infty, \infty)
  • BR−{3}\displaystyle \mathbb{R} - \{3\}
  • C(−∞,0)\displaystyle (-\infty, 0)
  • D(0,−∞)\displaystyle (0, -\infty)

Detailed Solution & Explanation

We are given the function:
f(x)=3x−2f(x) = 3x - 2
By default, unless specified otherwise, the domain of a polynomial function like a linear function is the set of all real numbers R\displaystyle \mathbb{R} or (−∞,∞)\displaystyle (-\infty, \infty).
Since f(x)=3x−2\displaystyle f(x) = 3x - 2 is a non-constant linear function, for any real number y\displaystyle y, we can find a corresponding real number x\displaystyle x such that:
y=3x−2  ⟹  x=y+23y = 3x - 2 \implies x = \frac{y + 2}{3}
Since x∈R\displaystyle x \in \mathbb{R} for every y∈R\displaystyle y \in \mathbb{R}, every real number is mapped by the function. Thus, the range of the function is the set of all real numbers R\displaystyle \mathbb{R}, which is written in interval notation as (−∞,∞)\displaystyle (-\infty, \infty).
Hence, **Option A** is the correct answer.

About This Chapter: Sets, Relations and Functions

Paper

Paper 3: Quantitative Aptitude

Weightage

3-5 Marks

Key Topics

Sets, Relations, Functions

This chapter covers Sets, Relations, Functions and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 3-5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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