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Functional Question (Posted on 2017-01-10)

If f(x) = 3f(1-x) + 1 for all x, what is the value of f(2017)?

From New Jersey Math League High School Contest Number 2 (November, 2016).

Submitted by Charlie

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Solution: (Hide)

f(a) = 3f(1-a) + 1
f(1-a) = 3f(a) + 1
f(a) = 3(3f(a) + 1) + 1
= 9f(a) + 3 + 1
= 9f(a) + 4

8 f(a) = - 4
f(a) = - 1/2 for any a, including 2017.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Generalizing	Steve Herman	2017-01-11 10:01:51
solution	xdog	2017-01-10 18:00:34

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