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

1 Answer
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