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Question 352624: Given two functions f(x)=2x-5 and g(x)=x^2. Are the following statements true or false. Could you explain as to how you got the answer. And if my answers are correct.
a) f(x) + g(x) = g(x) + f(x) My answer gx^2 +2fx-5f
b) f(x) - g(x) = g(x) - f(x) Not sure
c) f(2) + f(3) = f(5) My answer f(2)(2x-5)+f(3)(2x-5)=10fx-25f
d) f(0) is always equal to zero. My answer 0 zero
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! "Given two functions f(x)=2x-5 and g(x)=x^2. Are the following statements true or false. Could you explain as to how you got the answer. And if my answers are correct.
a) f(x) + g(x) = g(x) + f(x) My answer gx^2 +2fx-5f
b) f(x) - g(x) = g(x) - f(x) Not sure
c) f(2) + f(3) = f(5) My answer f(2)(2x-5)+f(3)(2x-5)=10fx-25f
d) f(0) is always equal to zero. My answer 0 zero"
f(x) = 2x - 5 and g(x) = x^2
on c) and d) you are subsituting in values for x
a) f(x) + g(x) = g(x) + f(x) = 2x - 5 + x^2 = x^2 + 2x - 5
true, just rearranging terms
b) f(x) - g(x) = 2x - 5 - x^2
g(x) - f(x) = x^2 - 2x + 5
false, 2 different results
c) f(2) + f(3) = 2(2) - 5 + 2(3) - 5 = 4 - 5 + 6 - 5 = 10 - 10 = 0
f(5) = 2(5) - 5 = 10 - 5 = 5
false, 2 different results
d) f(0) = 2(0) - 5 = 0 - 5 = -5
false, -5 is not 0 (not zero)
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