Let f and g 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,oo)to[0,oo)a n dg:[0,oo)to[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.

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

If f(x)a n dg(x) are two positive and increasing functions, then which of the following is not always true? (a) [f(x)]^(g(x)) is always increasing (b) [f(x)]^(g(x)) is decreasing, when f(x) 1,t h e n[f(x)]^(g(x)) is increasing.

The function f(x)= tan^(-1) (sin x + cos x ), x gt 0 is always an increasing function on the interval-

let h(x)=f(x)-[f(x)]^(2)+[f(x)]^(3) for every real number x. Prove that h(x) is increasing or decreasing according as f(x) is increasing or decreasing.

If fogoh(x) is an increasing function, then which of the following is not possible? (a) f(x),g(x),a n dh(x) are increasing (b) f(x)a n dg(x) are decreasing and h(x) is increasing (c) f(x),g(x),a n dh(x) are decreasing

If f(x) is differentiable and strictly increasing function, then the value of lim_(xto0)(f(x^2)-f(x))/(f(x)-f(0)) is

Let f(x)=xsqrt(4a x-x^2),(a >0)dot Then f(x) is (a). increasing in (0,3a) decreasing in (3a, 4a) (b). increasing in (a, 4a) decreasing in (5a ,oo) (c). increasing in (0,4a) (d). none of these

f: R to R ,f(x) is differentiable such that f(f(x))=k(x^5+x),k!=0)dot Then f(x) is a) always increasing (b) decreasing either increasing or decreasing c) non-monotonic

Let f be a twice differentiable function such that f"(x) = -f(x) , and f'(x) = g(x) , h(x)=[f(x)]^2+[g(x)]^2 Find h(10), if h(5) = 11