How do you find the inverse of #f(x)=ln(9x+7)#?

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Answer 1 · 2015-10-19T08:47:52

#x=(e^y-7)/9#

You need to isolate the #x# terms, so:

#y=ln(9x+7)#

Take the exponential on both sides:

#e^y=e^{ln(9x+7)}#

But #e^ln(z)=z#, so it becomes

#e^y=9x+7#

Subtract #7# from both sides:

#e^y-7 = 9x#

Divide both sides by #9#:

#(e^y-7)/9 = x#.