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)#