A certain function f has the property that f(x+y)=
f(x)+f(y) for all values of x and y. Which of the
following statements must be true when a=b?
I. f(a+b)=2f(a).
II. f(a+b)=[f(a] to the power of 2.
III. f(b) +f(b)=f(2a)

The problem ask to choose among the following statement that tells the truth about the said function f and the best answer among the following statement is in statement I. f(a+b)=2f(a) and statement III. f(b)+f(b) = f(2a). I hope you are satisfied with my answer and feel free to ask for more

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A certain function f has the property that f(x+y)= f(x)+f(y) for all values of x and y. Which of the following statements must be true when a=b? I. f(a+b)=2f(a). II. f(a+b)=[f(a] to the power of 2. III. f(b) +f(b)=f(2a)

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A certain function f has the property that f(x+y)=
f(x)+f(y) for all values of x and y. Which of the
following statements must be true when a=b?
I. f(a+b)=2f(a).
II. f(a+b)=[f(a] to the power of 2.
III. f(b) +f(b)=f(2a)