math contest question (function)
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pka
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\(\displaystyle f(a)=f(a+0)=f(a)f(0)\)
Thinking aloud
Taking both the statement as a property and the qualification of f(x) > 0, is there any other function that has this property than the exponential function in which case f(0) = 1 for any base. I don't know, shooting from the hip but I have my steel toed boots on.
I don't know how to solve this question
Given that f(a+b)=f(a)f(b) and f(x) is always positive, what is the value of f(0)?
Taking both the statement as a property and the qualification of f(x) > 0, is there any other function that has this property than the exponential function in which case f(0) = 1 for any base. I don't know, shooting from the hip but I have my steel toed boots on.