Since (f/g)(x) = f(x)/g(x) for x to be in the domain of (f/g)(x) it must be in the domain of f and in the domain of g. You also need to insure that g(x) is not zero since f(x) is divided by g(x). Thus there are 3 conditions. x must be in the domain of f: f(x) = 3x -5 and all real numbers x are in the domain of x.
Given f(x) = 2x + 3 and g(x) = –x2 + 5, find ( f o f )(x). ( f o f )(x) = f ( f (x)) = f (2x + 3) = 2( ) + 3 ... setting up to insert the input = 2(2x + 3) + 3 = 4x + 6 + 3 = 4x + 9 Given f(x) = 2x + 3 and g(x) = –x2 + 5, find (g o g)(x). (g o g)(x) = g(g(x)) = –( )2 + 5 ... setting up to insert the input = –(–x2 + 5)2 + 5 = –(x4 – 10x2 + 25) + 5 = –x4 + 10x2 – 25 + 5 = –x4 + 10x2 – 20