How do you find the inverse of $f(x) =ln(x^2)$ ?

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Answer 1 · 2015-12-23T16:12:07

Rewrite as

$y=ln(x^2)$

Switch the $x$ and $y$ and solve for $y$ .

$x=ln(y^2)$

Use the properties of logarithms.

$x=2ln(y)$

$x/2=ln(y)$

To undo the natural logarithm, exponentiate with base $e$ .

$e^(x/2)=e^(ln(y))$

$e^(x/2)=y$

This can be written in function notation.

$f^-1(x)=e^(x/2)$

How do you find the inverse of f(x) =ln(x^2)f(x) =ln(x^2)?