Question 52462: f(x)=2/3x+6
g(x)=3/2x-9
determine whether f)x) and g(x) are inverses of each other
my ans. is yes am I right? Answer by funmath(2933) (Show Source):
You can put this solution on YOUR website! Yes you're right.
The way to find out if functions are inverses of each other is to check and see if their composite functions are equal to x. Also make sure the functions are one to one functions.
(fog)(x)=f(g(x))=f(3/2x-9)
f(3/2x-9)=2/3(3/2x-9)+6
=(2/3)(3/2)x+(2/3)(-9/1)+6
=x-18/3+6
=x-6+6
=x
(gof)(x)=g(f(x))=g(2/3x+6)
g(2/3x+6)=3/2(2/3x+6)-9
=(3/2)(2/3)x+(3/2)(6/1)-9
=x+18/2-9
=x+9-9
=x
Since (fog)(x)=(gof)(x)=x, you know that they are inverse functions of each other.
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