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Verify that the functions f and g are inverses of each other by showing that f(g(x))=x...

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libbysimone | (Level 1) Salutatorian

Posted January 13, 2012 at 10:10 AM via web

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Verify that the functions f and g are inverses of each other by showing that f(g(x))=x g(f(x))=x f(x)=2/x+6 g(x)=2/(x-6).  Please show all your work.

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted January 13, 2012 at 10:53 AM (Answer #1)

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Given `f(x)=2/x+6` and `g(x)=2/(x-6)` , show that `f` and `g` are inverses by showing that `f(g(x))=g(f(x))=x` .

(1) `f(g(x))=2/(2/(x-6))+6`

`=(2(x-6))/2+6` Multiply num and den by x-6

`=x-6+6`

`=x`

(2) `g(f(x))=2/(2/x+6-6)`

`=2/(2/x)`

`=x`

 

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