Official Quant Book - p72, #17

[Alexander]

Hi - I don't understand the explanation given in the answer section.

Question: The function f has the property that f(x) = f( X + 1) for all numbers. If f(4) = 17, what is the value of f(8)?

Thanks,
Alexander

[tommywallach]

Hey Alexander,

Remember, functions represent an input/output situation. In the formulation f(x), the x represents the input, and the f(x) represents the output.

If f(x) = f(x+1), then you know that inputting a given x value will provide the same output as if you'd inputted x + 1. If that's true, then inputting 1.1 would be the same as inputting 2.1. Inputting 100 would the same as inputting 99. So if inputting 4 gets you an output of 17, then inputting 5 would also get you an output of 17, as would inputting 6, or 7, or 8. So the answer is 17.

Hope that helps!

-t