f(a+b) = f(a) + f(b)
Insert a and b in the answer options
f(x) = x^2
f(a+b) = (a+b)^2
f(a) = a^2
f(b) = b^2
(a+b)^2 is not equal to a^2 + b^2
Therefore we have to find the value for f(x) which hold true for f(a+b) = f(a) + f(b)
After pluggin in the a and b for x in all the options you will find that only Option E holds true.
f(x) = -3x
f(a+b)= -3(a+b) = -3a - 3b
f(a) = -3a
f(b) = -3b
-3a - 3b = -3a + (-3b) = -3a - 3b
Hence E is the answer
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