Question

If f(x) = \(\rm\frac{x}{x-1}\), then \(\rm \frac{f(a)}{f\left(\frac{1}{a}\right)}\) = ?
1. 1
2. a
3. \(\rm\frac1a\)
4. -a

Answer 1

Correct Answer - Option 4 : -a

Concept:

Real Functions:

If f(x) = a0x0 + a1x1 + a2x2 + ... anxn, where a0, a1, ... an are constants, then, f(y) = a0y0 + a1y1 + a2y2 + ... anyn.

Calculation:

Given that f(x) = \(\rm\frac{x}{x-1}\).

∴ f(a) = \(\rm\frac{a}{a-1}\) and \(\rm f\left(\frac1a\right)=\frac{\frac1a}{\frac1a-1}=\frac{1}{1-a}\).

Now, \(\rm \frac{f(a)}{f\left(\frac{1}{a}\right)}=\frac{\frac{a}{a-1}}{\frac{1}{1-a}}\) = -a.