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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Functions

NDA 2019 · Mathematics · Functions

If f(x)=(x-2)/(x+2), x ≠-2 , then what is ^ -1 (x) equal to ?

If f(x)=x−2x+2,x≠−2\mathrm{f}(\mathrm{x})=\frac{x-2}{x+2}, x \neq-2, then what is \mathrmf−1(x)\mathrmf^{-1}(\mathrm{x}) equal to ?

Options

  1. A4(x+2)x−2\frac{4(x+2)}{x-2}
  2. Bx+24(x−2)\frac{x+2}{4(x-2)}
  3. Cx+2(x−2)\frac{x+2}{(x-2)}
  4. D2(1+x)1−x\frac{2(1+x)}{1-x}

Correct answer

D. 2(1+x)1−x\frac{2(1+x)}{1-x}

Step-by-step solution

f(x)=y=\frac{x-2}{x+2}, x \neq-2y1=x−2x+2⇒y+1y−1=x−2+x+2x−2−x−2⇒y+1y−1=2x−4⇒y+1y−1=−x2⇒x=−2(y+1y−1)\begin{aligned} & \frac{y}{1}=\frac{x-2}{x+2} \Rightarrow \frac{y+1}{y-1}=\frac{x-2+x+2}{x-2-x-2} \\ & \Rightarrow \frac{y+1}{y-1}=\frac{2 x}{-4} \\ & \Rightarrow \frac{y+1}{y-1}=\frac{-x}{2} \Rightarrow x=-2\left(\frac{y+1}{y-1}\right)\end{aligned}Now,Now,\mathrm{y}=\frac{-2(x+1)}{x-1}=\frac{2(x+1)}{1-x}
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