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 (a)always zero (b) always negative always positive (d) strictly increasing none of these

Let f:[0,,∞) rarr [0,,∞)and g:[0,,∞) rarr [0,,∞) be non increasing and non decreasing functions respectively and h(x) =g(f(x)). If h(0)=0 .Then show h(x) is always identically zero.

Show that f(x)=1/x is decreasing function on (0,oo)dot

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

If f:[1,10]->[1,10] is a non-decreasing function and g:[1,10]->[1,10] is a non-increasing function. Let h(x)=f(g(x)) with h(1)=1, then h(2)

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).

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

The function f and g are positive and continuous. If f is increasing and g is decreasing, then int_0^1f(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

The function f and g are positive and continuous. If f is increasing and g is decreasing, then int_0^1f(x)[g(x)-g(1-x)]dx is always non-positive is always non-negative can take positive and negative values none of these

Let f(x) be a non-constant twice differentiable function defined on (oo, oo) such that f(x) = f(1-x) and f"(1/4) = 0 . Then