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Let f : [0,1] R be such that f(xy)=f(x).f(y) for all x,y, [0,1], andf(0) 0.  If y=y(x) satisfies the differential equation, =f(x)  with  y(0)=1, then y y  is equal to

a.

4

b.

3

c.

5

d.

2


Question ID - 56767 | Toppr Answer

Let f : [0,1] R be such that f(xy)=f(x).f(y) for all x,y, [0,1], andf(0) 0.  If y=y(x) satisfies the differential equation, =f(x)  with  y(0)=1, then y y  is equal to

a.

4

b.

3

c.

5

d.

2

1 Answer - 5876 Votes

3537

Answer Key : (b) -

f(xy)=f(x).f(y)

f(0)=1 as f(0) 0

 f(x)=1

 = f(x)=1

y = x+c

At, x=0, y=1 c=1

y=x+1

y y +1+ +1=3



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