How do you find the inverse of f(x)= 1/3x + 2 and is it a function?

1 Answer
Alan P.
Jul 18, 2016

color(blue)(g(x)=3x-6) is a function
(which is the inverse of f(x)=1/3x+2)

Explanation:

If g(x) is the inverse of f(x)
then by definition
color(white)("XXX")g(f(x))=x
and
color(white)("XXX")f(g(x))=x

Since f(color(red)(x))=1/3color(red)(x)+2
then
color(white)("XXX")f(color(red)(g(x)))=1/3color(red)(g(x))+2

But from our original definition we know that
color(white)("XXX")f(g(x))=x

Therefore
color(white)("XXX")f(g(x))=1/3g(x)+2=x

color(white)("XXX")rArr1/3g(x)=x-2

color(white)("XXX")rArrg(x)=3x-6

Since any value of x gives a single value for g(x)
it follows that g(x) is a function.

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