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Increasing and decreasing Functions

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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.

If y = f(x) be a monotonically increasing or decreasing function of x and M is the median of variable x, then the median of y is

Statement 1 The equation a^(x)+b^(x)+c^(x)-d^(x)=0 has only real root, if agtbgtcgtd . Statement 2 If f(x) is either strictly increasing or decreasing function, then f(x)=0 has only real root.

The function f(x)=x^2-x+1 is increasing and decreasing in the intervals

If f is decreasing and g is increasing functions such that gof exists then gof is

if f is an increasing function and g is a decreasing function on an interval I such that fog exists then

Show that f(x)=cosx is a decreasing function on (0,\ pi) , increasing in (pi,\ 0) and neither increasing nor decreasing in (pi,\ pi) .

Show that f(x)=cosx is decreasing function on (0,pi), increasing in (-pi,0) and neither increasing nor decreasing in (-pi,pi)dot

Prove that the function f defined by f(x)=x^2−x+1 is neither increasing nor decreasing in (−1,1) . Hence find the intervals in which f(x) is strictly increasing and strictly decreasing.

If x in (0,pi/2) , then the function f(x)= x sin x +cosx +cos^(2)x is (a) Increasing (b) Decreasing (c) Neither increasing nor decreasing (d) None of these