If f(x) = \(\frac{x}{x-1}\) , then \(\frac{f(a)}{f(a+1)} \) equals

1.	If f(x) = \(\frac{x}{x-1}\) , then \(\frac{f(a)}{f(a+1)} \) equals(a) \(f\big(\frac{1}{a}\big)\) (b) f (a)2 (c) f (– a) (d) f (0)
Answer» Answer: (b) = f (a)² Given, f(x) = \(\frac{x}{x-1}\) ⇒ \(\frac{f(a)}{f(a+1)} = \frac{\frac{a}{a-1}}{\frac{a+1}{a+1-1}}\) = \(\frac{a}{a-1} \times \frac{a}{a+1} = \frac{a^2}{a^2-1}\) = \(f(a^2)\) .

If f(x) = \(\frac{x}{x-1}\) , then \(\frac{f(a)}{f(a+1)} \) equals(a) \(f\big(\frac{1}{a}\big)\) (b) f (a)2 (c) f (– a) (d) f (0)

Answer»

Answer: (b) = f (a)²

Given,

f(x) = \(\frac{x}{x-1}\)

⇒ \(\frac{f(a)}{f(a+1)} = \frac{\frac{a}{a-1}}{\frac{a+1}{a+1-1}}\)

= \(\frac{a}{a-1} \times \frac{a}{a+1} = \frac{a^2}{a^2-1}\)

= \(f(a^2)\) .