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Suppose $f (x ) = x^2 + 12$. If $m > 0$ and $f (3m) = 3(f (m))$, what is the value of $m$?

Suppose $$f (x ) = x^2 + 12$$. If $$m > 0$$ and $$f (3m) = 3(f (m))$$, what is the value of $$m$$?

Mar 10, 2019

$$(3m)^2 + 12 = 3(m^2 + 12)\\ 9m^2 + 12 = 3m^2 + 36\\ 6m^2-24=0\\ m^2 - 4 = 0\\ \text{I leave you to finish}$$