f(x)=e^(-f)" for all "x in R,g(x)={[x^(2),,x<(1)/(2)],[x-(1)/(4),,x>=(1)/(2)]" and "h(x)=f(g(x))" .Then derivative of "h(x)" at "

Let f(x)=e^(x),g(x)={:{(x^(2),if,xlt(1)/(2)),(x-(1)/(4),if,xge(1)/(2)):} and h(x)=f(g(x)) . The derivative of h(x) and x=(1)/(2) is e^((1)/(a)) then a equal to

f(x)= x, g(x)= (1)/(x) and h(x)= f(x) g(x). If h(x) = 1 then…….

Suppose f, g, and h be three real valued function defined on R. Let f(x) = 2x + |x|, g(x) = (1)/(3)(2x-|x|) and h(x) = f(g(x)) The domain of definition of the function l (x) = sin^(-1) ( f(x) - g (x) ) is equal to

Suppose f, g, and h be three real valued function defined on R. Let f(x) = 2x + |x|, g(x) = (1)/(3)(2x-|x|) and h(x) = f(g(x)) The domain of definition of the function l (x) = sin^(-1) ( f(x) - g (x) ) is equal to

Suppose f, g, and h be three real valued function defined on R. Let f(x) = 2x + |x|, g(x) = (1)/(3)(2x-|x|) and h(x) = f(g(x)) The domain of definition of the function l (x) = sin^(-1) ( f(x) - g (x) ) is equal to

Given f(x)=(1)/(1-x),g(x)=f{f(x)} and h(x)=f{f{f(x)}} then the value of f(x)g(x)h(x) is

If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)=g(x).g(y)+f(x).f(y) for all x in R. If right handed derivative at x=0 exists for f(x) find the derivative of g(x) at x=0