Question

Suppose we are given two functions, say r(x) and s(x).
a) Is it true that r(x) + s(x) = s(x) + r(x) for all values of x? Why or why not?
b) Is it true that r(x) s(x) = s(x) r(x) for all values of x? Why or why not?
c) Is it true that r(0) = 0? Why or why not?

Answer 1

a and b are correct because suppose r(x)= 2+x and s(x) = 7+2x
r(x) + s(x) = s(x) + r(x). The order in which you add or multiply would not change the functions themselves. You can try this by using simple functions such as r(x)=2 and s(x)=3
3+2=5 and 2+3=5 the order didn't change anything. 2.3=6 and 3.2=6
But for saying r(0) = 0 is a big assumption, assuming r(x) = 7+2x r(0) = 7.
Hope that helps.

Answer 2

thanks for the help beeqay!!!