SOLUTION: Hi, I am having problems understanding a problem based on the rule of a function. The question is:
If a function f(x) always satisfies such a property that f(a+b)=f(a)+f(b) for al
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-> SOLUTION: Hi, I am having problems understanding a problem based on the rule of a function. The question is:
If a function f(x) always satisfies such a property that f(a+b)=f(a)+f(b) for al
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Question 1072079: Hi, I am having problems understanding a problem based on the rule of a function. The question is:
If a function f(x) always satisfies such a property that f(a+b)=f(a)+f(b) for all real number a and b and f(1)=2, then find the value of f(3).
if a=1 and b=1, then f(1+1)=f(1)+f(1) so this is f(2) and this would be where f(1)=2 is derived from as I understand it.
Then I would have to find a set of numbers that would =3 when solving for f(3) and sub those in to the function formula given.
f(1+2)=f(1)+f(2) and now is where I get lost because the answer I am supposed to get is f(3) = f(1+2)=f(1)+f(2) = 2+4=6
Is this now saying that I would multiply by 2?(i.e f(1+2) = 2[f(1)]+2[f(2)])
I guess since f(1)=2 that is why and if it were f(1)=5 then I would multiply the respective numbers by 5? (i.e f(2+3) = 5[f(2)]+5[f(3)])
Thank you for any insight you can provide
