If g(x) is monotonically increasing and f(x) is monotonically decreasing for x R and if (gof) (x) is defined for x e R, then prove that (gof)(x) will be monotonically decreasing function. Hence prove that` (gof) (x +1)leq (gof) (x-1). `

If g(x) is monotonically increasing and f(x) is monotonically decreasing for x in R and if (gof) (x) is defined for x in R , then prove that (gof)(x) will be monotonically decreasing function. Hence prove that (gof) (x +1)leq (gof) (x-1).

f(x)=|xlog_(e )x| monotonically decreases in

f(x) = |x log_(e) x| monotonically decreases in

Let f(x) =x - tan^(-1)x. Prove that f(x) is monotonically increasing for x in R

Let f(x) =x - tan^(-1)x. Prove that f(x) is monotonically increasing for x in R

Let f(x) =e^(2x) -ae^(x)+1. Prove that f(x) cannot be monotonically decreasing for AA x in R for any value of a

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

In the interval (1,\ 2) , function f(x)=2|x-1|+3|x-2| is (a) monotonically increasing (b) monotonically decreasing (c) not monotonic (d) constant

If f:RtoR and g:RtoR defined by f(x)=x^2 and g(x)=x+1 , then gof(x) is