Let f:x rarry satisfy f(x)f(y)=f(xy) for...

Let `f:x rarry` satisfy f(x)f(y)=f(xy) for all real numbers x and y. If f(1) =1 and f(2)=4, then `f((1)/(2))`= - a) 0 b)1/4 c)1/2 d)1

A

0

B

`(1)/(4)`

C

`(1)/(2)`

D

1

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

If a function f satisfies f{f (x)}=x+1 for all real values of x and if f(0)=1/2 then f(1) is equal to a) 1/2 b)1 c) 3/2 d)2

Let f (x + y) = f(x ). f( y ) for all x and y . If f (3 ) = 3 and f ' (0) =11, then f'(3 ) is equal to a)11 b)22 c)33 d)44

If f(x+y)=f(x)f(y) for all x and y, f(6)=3 and f'(0)=10, then f'(6) is :a)30 b)13 c)10 d)0

If f(x)=2x^(2)+bx+c and f(0)=3 and f(2)=1 , then f(1) is equal to a)1 b)2 c)0 d) 1/2

If f(1)=1,f'(1)=2 , then lim_(xto1)(sqrt(f(x))-1)/(sqrt(x)-1) is a)2 b)4 c)1 d) 1/2

A function f: RrarrR satisfies the equation f(x) f(y) - f(xy) = x+ y, AAx,y in R and f(1) gt 0 , then

If f(x) = |x-2| + |x+1| - x , then f'(-10) is equal to a)-3 b)-2 c)-1 d)0

Let f(x+1/y)+f(x-1/y)=2 f(x)f(1/y)AAxy in R, y ne 0 and f(0) = 0 then the value of f(1) + f(2) = a) -1 b)0 c)1 d)none of these