Let `fa n dg` be increasing and decreasing functions, respectively, from `[0,oo]to[0,oo]dot` Let `h(x)=f(g(x))dot` If `h(0)=0,` then `h(x)-h(1)` is always zero (b) always negative always positive (d) strictly increasing none of these

Let f (x ) and g(x) be increasing and decreasing functions respectively from [0,oo) "to" [ 0 , oo) Let h (x) = fog (x) If h(0) =0 then h(x) is

Show that the function f(x)=x^(2) is strictly increasing function on [0,oo)

Show that the function f(x)=x^(2) is a strictly increasing function on (0,oo).

Let f:[0,oo)rarr[0,oo) and g:[0,oo)rarr[0,oo) be non-increasing and non-decreasing functions,respectively,and h(x)=g(f(x)) If f and g are differentiable functions,h(x)=g(f(x)). If f and g are differentiable for all points in their respective domains and h(0)=0, then show h(x) is always, identically zero.

The function f and g are positive and continuous.If f is increasing and g is decreasing,then int_(0)^(1)f(x)[g(x)-g(1-x)]dx (a)is always non-positive (b)is always non- negative ( c) can take positive and negative values (d)none of these

Prove that function f(x)=log_(e)x is strictly increasing in the interval (0,oo)

Prove that function f(x)=log_(e)x is strictly increasing in the interval (0,oo)

Show that the function f(x ) = |x| is (a) striclty increasing on [0, oo] (b) strictly decreasing on [-oo, 0]

Let f(x) be a increasing function defined on (0,\ oo)dot If f(2a^2+a+1)>f\ (3a^2-4a+1)dot Find the range of adot

The function f(x)=(x)/(1+|x|) is (a) strictly increasing (b) strictly decreasing (c) neither increasing nor decreasing (d) none of these