How do you find the inverse of #y=e^(x-1)#?

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Answer 1 · 2015-12-06T03:36:36

#f^(-1)(x) = ln x +1#

Given #y= e^(x-1)# (this is a one-to-one function)

Step 1: Switch #x# for #y# and #y# for #x# like this

#color(red) x= e^(color(blue)(y)-1)#

Step 2: Begin to solve for #y#

Take #ln# of both side

#ln(x) = lne^(y-1)#

Use the properties of log
#ln e= 1# ; # log a^n = nlog a#

#ln x= y-1#

#ln x + 1 = y#

Step 3: Change #y# to #f^(-1)(x) #

#f^(-1)(x) = ln x +1#

*Note: To solve exponential equation, we use logarithm, and vice versa

*Remember: One-to-one function is the only function that have an i nverse that is an function.