Home
Class 12
MATHS
Let f(x) be defined for all x > 0 and be...

Let `f(x)` be defined for all `x > 0` and be continuous. Let `f(x)` satisfies `f(x/y)=f(x)-f(y)` for all `x,y and f(e)=1.` Then (a) `f(x)` is bounded (b) `f(1/x)vec 0` as `x vec0` (c) `f(x)` is bounded (d) `f(x)=(log)_e x`

Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x) be defined for all x > 0 and be continuous. Let f(x) satisfies f(x/y)=f(x)-f(y) for all x,y and f(e)=1. Then (a) f(x) is unbounded (b) f(1/x)vec 0 as x vec0 (c) f(x) is bounded (d) f(x)=(log)_e x

Let f(x) be defined for all x > 0 and be continuous. Let f(x) satisfies f(x/y)=f(x)-f(y) for all x,y and f(e)=1. Then (a) f(x) is unbounded (b) f(1/x)vec 0 as x vec0 (c) f(x) is bounded (d) f(x)=(log)_e x

Let f(x) be defined for all x>0 and be continuous.Let f(x) satisfies f((x)/(y))=f(x)-f(y) for all x,y and f(e)=1. Then (a) f(x) is bounded (d) (b) f((1)/(x))vec 0 as xvec 0 (c) f(x) is bounded (d) f(x)=(log)_(e)x

Let f(x) be defined for all x > 0 and be continuous. Let f(x) satisfy f((4x)/y)=f(x)-f(y) for all x,y and f(4e) = 1, then (a) f(x) = In 4x(b) f(x) is bounded (c) lim_(x->0) f(1/x)=0 (d) lim_(x->0)xf(x)=0

Let f(x) be defined for all x>0 and be continuous.Let f(x) satisfy f((4x)/(y))=f(x)-f(y) for all x,y and f(4e)=1, then (a) f(x)=ln4x( b) f(x) is bounded (c) lim_(x rarr0)f((1)/(x))=0 (d) lim_(x rarr0)xf(x)=0