How do you find the inverse of #f(x)=log_3(x-4)-2#?

1 Answer
Alan P.
Dec 16, 2015

#barf(x) = 3^(x+2)+4#

Explanation:

Let #barf(x)# be the inverse of #f(x)=log_3(x-4)-2#

By definition of an inverse:
#color(white)("XXX")f(barf(x))=x#

Therefore
#color(white)("XXX")f(barf(x)) = log_3(barf(x)-4)-2 = x#

#color(white)("XXX")log_3(barf(x)-4) = x+2#

and since #(log_b a = c) hArr (b^c=a)#
#color(white)("XXX")3^(x+2) = barf(x)-4#

#color(white)("XXX")barf(x) = 3^(x+2) + 4#

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