How do you find the inverse of #f(x)= (x+5)^3-7#?

1 Answer
Alan P.
Dec 21, 2015

#bar(f(x)) = root(3)(x+7)-5#

Explanation:

If #bar(f(x))# is the inverse of #f(x)#
then by definition:
#color(white)("XXX")f(bar(f(x))) = x#

So
#color(white)("XXX")f(bar(f(x))) = (bar(f(x))+5)^3-7=x#

#color(white)("XXXXXXXXXX")bar(f(x))+5 color(white)("XXXX")= root(3)(x+7)_#

#color(white)("XXXXXXXXXX")bar(f(x))color(white)("XXXXXX") = root(3)(x+7)-5#

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