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BITSAT 2023Paper 2
Exam
BITSAT
Year
2023
Paper
Paper 2
Subject
Mathematics
Chapter
Functions

BITSAT 2023 · Paper 2 · Mathematics · Functions

Consider the function f in A=R-\ (2)/(3)\ defined as f(x)=(4...

Consider the function f\mathrm{f} in A=R−{23}\mathrm{A}=\mathrm{R}-\left\{\frac{2}{3}\right\} defined as f(x)=4x+36x−4f(x)=\frac{4 x+3}{6 x-4}, then f−1f^{-1} is equal to

Options

  1. A3+4x6x−4\frac{3+4 x}{6 x-4}
  2. B6x−43+4x\frac{6 x-4}{3+4 x}
  3. C3−4x6x−4\frac{3-4 x}{6 x-4}
  4. D9+2x6x−4\frac{9+2 x}{6 x-4}

Correct answer

A. 3+4x6x−4\frac{3+4 x}{6 x-4}

Step-by-step solution

Given f(x)=4x+36x−4f(x)=\frac{4 x+3}{6 x-4}
Let y=4x+36x−4y=\frac{4 x+3}{6 x-4},
⇒6xy−4y=4x+3⇒x(6y−4)=3+4y⇒x=3+4y6y−4f−1(x)=3+4x6x−4\begin{aligned} \\ & \Rightarrow 6 x y-4 y=4 x+3 \Rightarrow x(6 y-4)=3+4 y \\ \\ & \Rightarrow x=\frac{3+4 y}{6 y-4} \\ \\ & f^{-1}(x)=\frac{3+4 x}{6 x-4} \\ \end{aligned}
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