How do you find the inverse of #f(x)=log[x+1]#?

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Answer 1 · 2018-06-26T21:04:24

#f^(-1)(x) = e^x -1 #

# y = log[ x+1 ] #

Swap #x# for the #y#

#x = log[y+1] #

Then rearrange for #y#

#e^x = e^log[y+1] #

#e^x = y +1 #

#e^x -1 = y #

#=> f^(-1) (x) = e^x -1 #

If you take #logx -= log_e x -= lnx #

If you work with #logx -= log_10 x #

The answer would just be # = 10^x -1 #