f(x) is a real valued function where f(xy) = [f(x)] + [f(y)] + f(x)f(y) for all real x,y. If f(2) = 1, then what is the value of f(1/2) ?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

–1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

-1/2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D -1/2
Option (e)
f(2) = f(2 x 1) = f(2) + f(1) + f(2).f(1) = 1
f(1) = 0

Suggest Corrections

Similar questions

Q. Let

f

be a real valued function satisfying

f (x + y) = f (x) + f (y)

for all

x, y .

f (1) = \frac{1}{2}

, then the value of

f (16)

A function $f : R \to [1, \infty)$ satisfies the equation $f (x y) = f (x) f (y) - f (x) - f (y) + 2$ . If f is differentiable on $R - 0 a n d f (2) = 5, f^{'} (x) = \frac{f (x) - 1}{x} . λ t h e n λ$ =________

Let $f : R^{+} \to R^{+}$ be a differentiable function satisfying $f (x y) = \frac{f (x)}{y} + \frac{f (y)}{x}$ for all $x, y ϵ R^{+}$ . Also $f (1) = 0, f^{'} (1) = 1$ . If M is the greatest value of $f (x)$ then $[m + e]$ is ___ (where [.] represents Greatest Integer Function).