Sets, Relations and FunctionsPYQ Sept 25Question 4135 of 145
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The inverse of the function f(x)=2+3xx+5\displaystyle f(x) = \frac{2+3x}{x+5}, by taking f(x)\displaystyle f(x) as y\displaystyle y, is

Options

A2+5yy+3\displaystyle \frac{2+5y}{y+3}
B2−5yy+3\displaystyle \frac{2-5y}{y+3}
C2−5yy−3\displaystyle \frac{2-5y}{y-3}
D2+5yy−3\displaystyle \frac{2+5y}{y-3}
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Correct Answer

✅ Option c — 2−5yy−3\displaystyle \frac{2-5y}{y-3}

All Options:

  • A2+5yy+3\displaystyle \frac{2+5y}{y+3}
  • B2−5yy+3\displaystyle \frac{2-5y}{y+3}
  • C2−5yy−3\displaystyle \frac{2-5y}{y-3}
  • D2+5yy−3\displaystyle \frac{2+5y}{y-3}

Detailed Solution & Explanation

Given function: y=2+3xx+5y = \frac{2+3x}{x+5}
To find the inverse function, we express x\displaystyle x in terms of y\displaystyle y: y(x+5)=2+3xy(x+5) = 2+3x xy+5y=2+3xxy + 5y = 2+3x
Isolate the terms with x\displaystyle x on one side of the equation: xy−3x=2−5yxy - 3x = 2 - 5y Factor out x\displaystyle x: x(y−3)=2−5yx(y-3) = 2 - 5y x=2−5yy−3x = \frac{2-5y}{y-3}
Thus, the inverse function of y\displaystyle y is: f−1(y)=2−5yy−3f^{-1}(y) = \frac{2-5y}{y-3}
Hence, **Option C** 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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