Function of the form max {f(x) g(x) h(x) }

If f(x) be a function such that f(-x)= -f(x),g(x) be a function such that g(-x)= -g(x) and h(x) be a function such that h(-x)=h(x) , then choose the correct statement: I. h(f(g(-x)))=-h(f(g(x))) II. f(g(h(-x)))=f(g(h(x))) III. g(f(-x))=g(f(x))

Let f (x), g(x) be two real valued functions then the function h(x) =2 max {f(x)-g(x), 0} is equal to :

Let f (x), g(x) be two real valued functions then the function h(x) =2 max {f(x)-g(x), 0} is equal to :

If f(x) is a twice differentiable function such that f'' (x) =-f(x),f'(x)=g(x),h(x)=f^2(x)+g^2(x) and h(10)=10 , then h (5) is equal to

If f(x) is a twice differentiable function such that f'' (x) =-f,f'(x)=g(x),h(x)=f^2(x)+g^2(x) and h(10)=10 , then h (5) 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

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