Question 312796
HELP:
Given 2 functions f(x)-2x-5 and g(x)=x^2. Determine whether each of the following statements is true or false and why.
a) f(x)+g(x)= g(x)+f(x)
b) f(x)-g(x)= g(x)-f(x)
c) f(2)+f(3)= f(5)
d) f(0) is always equal to zero

f(x)= 2x - 5
g(x)= x^2
f(x) + g(x) = x^2 + 2x - 5
f(x) - g(x) = -x^2 + 2x - 5
g(x) + f(x) = x^2 + 2x - 5
g(x) - f(x) = x^2 - 2x + 5
f(2) = 2(2) - 5 = 4 - 5 = -1
f(3) = 2(3) - 5 = 6 - 5 = 1
f(5) = 2(5) - 5 = 10 - 5 = 5
f(2) + f(3) = -1 + 1 = 0
f(0) = 2(0) - 5 = -5
a) f(x)+g(x) = g(x)+f(x) --> true, no signs changed
b) f(x)-g(x) = g(x)-f(x) --> false, the signs are different
c) f(2)+f(3)= f(5) --> false, f(5) is 5, and f(2)+f(3)=0
d) f(0) is always equal to zero --> false, f(0) is -5