SOLUTION: 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)

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

Found 2 solutions by CharlesG2, rapaljer:
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
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

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
In stating this question, you forgot the equal sign for f(x). Did you mean
f(x)= 2x- 5 or did you mean f(x) = -2x -5?

In general, statement a) is always true.

Statement b) is NOT true for all values of x.

Statement c) is NOT generally true, but it could be true in specific cases.

Statement d) is NOT true.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

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