Suppose that the functions r and s are defined for all real numbers x as follows

Question

r(x)=4x+6

s(x)=3x

Answer 1

So what is the question? If they are defined for all real numbers, any operations can be done with them. Addition, subtraction, multiplication, division (if x is not 0), composition.

Answer 2

The rules for functions are the same as they'd be for adding or subtracting anything else. So if r(x)=4x+6

s(x)=3x, then we can solve for whatever x would be. Thus if we combine the r and s, we would get 7x + 6. Since all that is equal to 3x, we can equate the two with the shorter =. 7x + 6 = 3x. If we get all constants on one side and variable terms on the other, we get 6 = -4x. When we simplify, x = -6/4 or -3/2 if reduced.