BMAD 65 Posted September 22, 2017 Report Share Posted September 22, 2017 Find a continuous function where the following identity is true: f(2x) = 3f(x) Quote Link to post Share on other sites

2 ThunderCloud 5 Posted December 7, 2017 Report Share Posted December 7, 2017 (edited) 25 minutes ago, plasmid said: Sort of combining the two solutions already given Hide contents f(x) = C 3^{log}^{2}^{x} where C is any constant f(2x) = C 3^{log}^{2}^{(2x)} = C 3^{1+log}^{2}^{x} = C (3 3^{log}^{2}^{x}) = 3f(x) Spoiler I suspect the issue with this solution is that f(x) is not defined for all x, and therefore not continuous for all x. f(x) = 3^{log2(|x|)}almost works, but still has a discontinuity at x = 0. Edited December 7, 2017 by ThunderCloud Quote Link to post Share on other sites

1 Buddyboy3000 4 Posted September 24, 2017 Report Share Posted September 24, 2017 Spoiler I'm not too sure if this is right, but I got two possible solutions: y=3^(log(x)/log(2)) and y=-3^(log(-x)/log(2)) I got these two solutions by trying to make an equation where the y-value triples only when the x-value doubles, and not after each x-value. Quote Link to post Share on other sites

1 ThunderCloud 5 Posted December 5, 2017 Report Share Posted December 5, 2017 You asked for it... Spoiler f(x) = 0 Quote Link to post Share on other sites

0 plasmid 41 Posted December 7, 2017 Report Share Posted December 7, 2017 Sort of combining the two solutions already given Spoiler f(x) = C 3^{log}^{2}^{x} where C is any constant f(2x) = C 3^{log}^{2}^{(2x)} = C 3^{1+log}^{2}^{x} = C (3 3^{log}^{2}^{x}) = 3f(x) Quote Link to post Share on other sites

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## BMAD 65

Find a continuous function where the following identity is true: f(2x) = 3f(x)

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