Inverse Function of Logarithm

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The answer is A but I don't understand why!

$ -2 \log_e (x^2) $ can be re-written as $ -4 \log_e(x) $ right?

but why do these two graphs look different?

the graph $-2 \log_e (x^2) $ is one to one from $ x > 0 $ or $ x < 0 $... why $-1$?

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Hint:

the function should be

  1. defined so $x\ne0$
  2. one to one and onto so either $(-\infty, 0)$ i.e $m<0$ or $(0,\infty)$