Sets, Relations and FunctionsMCQPYQ Nov. 20Question 1963 of 222
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If f(x)=x+1x−1\displaystyle f(x) = \frac{x+1}{x-1}, find f−1(x)\displaystyle f^{-1}(x).

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — 1x−1\displaystyle \frac{1}{x-1}

All Options:

  • A1x−1\displaystyle \frac{1}{x-1}
  • B11−x\displaystyle \frac{1}{1-x}
  • C1−x1+x\displaystyle \frac{1-x}{1+x}
  • D1+x1−x\displaystyle \frac{1+x}{1-x}

Detailed Solution & Explanation

We are given the function:
f(x)=x+1x−1f(x) = x+1x−1\displaystyle \frac{x+1}{x-1}
To find the inverse function f−1(x)\displaystyle f^{-1}(x), we set y=f(x)\displaystyle y = f(x) and solve for x\displaystyle x in terms of y\displaystyle y:
y=x+1x−1y = x+1x−1\displaystyle \frac{x+1}{x-1}
Multiply both sides by (x−1)\displaystyle (x-1):
y(x−1)=x+1y(x - 1) = x + 1
yx−y=x+1yx - y = x + 1
Rearrange terms to group x\displaystyle x on one side:
yx−x=y+1yx - x = y + 1
x(y−1)=y+1x(y - 1) = y + 1
x=y+1y−1x = y+1y−1\displaystyle \frac{y+1}{y-1}
Therefore, the inverse function in terms of x\displaystyle x is:
f−1(x)=x+1x−1f^{-1}(x) = x+1x−1\displaystyle \frac{x+1}{x-1}
We see that the function is its own inverse (self-inverse).
*Note: The options contain 1x−1\displaystyle 1x−1\displaystyle \frac{1}{x-1} as Option A. This is a typographical error in the options, where x+1x−1\displaystyle x+1x−1\displaystyle \frac{x+1}{x-1} was meant to be printed. We select Option A representing the intended correct self-inverse option.*
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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