If `f: RrarrR and g:RrarrR` are two given functions, then prove that `2min.{f(x)-g(x),0}=f(x)-g(x)-|g(x)-f(x)|`

If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and f(x)-g(x)=e^(-x) , then

If g is inverse of f then prove that f''(g(x))=-g''(x)(f'(g(x)))^(3).

Find fog, if f:RrarrR and g:RrarrR are given by: f(x)=cosxandg(x)=x^(2) .

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}

If f: R to R, g , R to R be two funcitons, and h(x) = 2 "min" {f(x) - g(x),0} then h(x)=

f:RrarrR given by f (x) = 2x is one-one function.

If f(x) and g(x) are two continuous functions defined on [-a,a], then the value of int_(-a)^(a){f(x)+f(-x)}{g(x)-g(-x)}dx is