v) What type of function is `y=f(x)/g(x)` ?

Following is the graph of y = f'(x) and f(0) = 0 . (a) What type of function y = f'(x) is ? Odd or even? (b) What type of function y = f(x) is ? Odd or even? (c) What is the value of int_(-a)^(a) f(x) dx ? (d) Has y = f(x) point of inflection? (e) What is the nature of y = f(x)? Monotonic or non-monotonic?

Identify the type of the functions: f(x)={g(x)-g(-x)}^(3)

If f(x+y)=f(x)dotf(y) for all real x , ya n df(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^2) is an even function.

If f(x+y)=f(x)dotf(y) for all real x , ya n df(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^2) is an even function.

Let [x] denote the integral part of x in R and g(x) = x- [x] . Let f(x) be any continuous function with f(0) = f(1) then the function h(x) = f(g(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 :

The figure above shows the graph of function f. If g(x)=-f(x) , which graph represents function g?

Consider the function f(x)={2x+3, x le 1 and -x^2+6, x > 1} Then draw the graph of the function y=f(x), y=f(|x|) and y=|f(x)|.

Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For all "x,y in R , where g(x) is continuous. Then,

Let f(x, y) be a periodic function satisfying f(x, y) = f(2x + 2y, 2y-2x) for all x, y; Define g(x) = f(2^x,0) . Show that g(x) is a periodic function with period 12.