A function g defined for all positive real numbers, satisfies `g'(x^2) =x^3` for all `xgt0` and `g(1)=1` Compute g (4).

A function is defined for all real numbers is defined for xgt0 as follows: f(x)={(x|x|, 0lexlt1), (2x, xge1):} How is f defined for xle0 If f is even

A function is defined for all real numbers is defined for xgt0 as follows: f(x)={(x|x|, 0lexlt1), (2x, xge1):} How is f defined for xle0 If f is odd

Given a function ' g' which has a derivative g' (x) for every real x and satisfies g'(0)=2 and g(x+y)=e^y g(x)+e^x g(y) for all x and y then: Find g(x).

Given a function ' g' which has a derivative g' (x) for every real x and satisfies g'(0)=2 and g(x+y)=e^y g(x)+e^y g(y) for all x and y then: Find g(x).

Given a function ' g' which has a derivative g' (x) for every real x and satisfies g'(0)=2 and g(x+y)=e^y g(x)+e^y g(y) for all x and y then:

Let the function f, g, h are defined from the set of real numbers RR to RR such that f(x) = x^2-1, g(x) = sqrt(x^2+1), h(x) = {(0, if x lt 0), (x, if x gt= 0):}. Then h o (f o g)(x) is defined by

Let the function f, g, h are defined from the set of real numbers RR to RR such that f(x) = x^2-1, g(x) = sqrt(x^2+1), h(x) = {(0, if x lt 0), (x, if x gt= 0):}. Then h o (f o g)(x) is defined by

Given a function ' g' which has a derivative g'(x) for every real x and satisfies g'(0)=2 and g(x+y)=e^(y)g(x)+e^(y)g(y) for all x and y then:

Consider f g and h are real-valued functions defined on R. Let f(x)-f(-x)=0 for all x in R, g(x) + g(-x)=0 for all x in R and h (x) + h(-x)=0 for all x in R. Also, f(1) = 0,f(4) = 2, f(3) = 6, g(1)=1, g(2)=4, g(3)=5, and h(1)=2, h(3)=5, h(6) = 3 The value of f(g(h(1)))+g(h(f(-3)))+h(f(g(-1))) is equal to

If a function g(x) which has derivaties g'(x) for every real x and which satisfies the following equation g(x+y) = e^(y)g(x) + e^(x)g(x) for all x and y and g'(0) = 2, then the value of {g'(x) - g(x)} is equal to