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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Functions

NDA 2017 · Mathematics · Functions

If f(x)= x x-1 , then what is f(a) f(a+1) equal to?

If f(x)=xx−1f(\mathrm{x})=\frac{\mathrm{x}}{\mathrm{x}-1}, then what is f(a)f(a+1)\frac{f(\mathrm{a})}{f(\mathrm{a}+1)} equal to?

Options

  1. Af(−aa+1)f \left(-\frac{\mathrm{a}}{\mathrm{a}+1}\right)
  2. Bf(a2)f \left(\mathrm{a}^2\right)
  3. Cf(1a)f \left(\frac{1}{\mathrm{a}}\right)
  4. Df(−a)f(-\mathrm{a})

Correct answer

B. f(a2)f \left(\mathrm{a}^2\right)

Step-by-step solution

f(x)=xx−1f(a)=aa−1f(a+1)=a+1a+1−1=a+1af(a)f(a+1)=aa−1a+1a=a2a2−1f(a2)=a2a2−1\begin{aligned} & f(x)=\frac{x}{x-1} \\ & f(a)=\frac{a}{a-1} \\ & f(a+1)=\frac{a+1}{a+1-1}=\frac{a+1}{a} \\ & \frac{f(a)}{f(a+1)}=\frac{\frac{a}{a-1}}{\frac{a+1}{a}}=\frac{a^2}{a^2-1} \\ & f\left(a^2\right)=\frac{a^2}{a^2-1}\end{aligned}
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