I will post a challenging math problem each day. The level of difficulty will vary, but most problems should not require any specialized knowledge beyond calculus. Problems are also posted on Twitter using the hashtag #mathpotd.
Monday, October 19, 2009
f(f(x)) = x^2
Find a real function f so that f(f(x)) = x^2 for all x.
How about f(x) = |x|^\sqrt{2}? Since we take the absolute value before exponentiating to an irrational power, f is defined for each real number x. Also, f(f(x)) = ||x|^\sqrt{2}|^\sqrt{2} = (|x|^\sqrt{2})^sqrt{2} = x^2.
How about f(x) = |x|^\sqrt{2}?
ReplyDeleteSince we take the absolute value before exponentiating to an irrational power, f is defined for each real number x.
Also, f(f(x)) = ||x|^\sqrt{2}|^\sqrt{2} = (|x|^\sqrt{2})^sqrt{2} = x^2.