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Determine if the two functions are inverses of one another.

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Determine if the two functions are inverses of one another.
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asked Jun 11, 2014 in PRECALCULUS by bilqis Pupil

1 Answer

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Note :

Two functions f (x) and g (x) are inverse functions if and only if both of their compositions are the identity function.

f o g (x) = g o f (x) = x.

The functions are f( x ) = 3x + 2 and g (x) = (x - 2)/3.

Now plug the formula for g(x) into every instance of "x" in the formula for f (x) :

f o g (x) = f (g (x) )

= f ( (x - 2)/3)

= 3(x - 2)/3 + 2

= x - 2 + 2

= x.

→ f o g (x) = x.

Now plug  the formula for f (x) into every instance of "x" in the formula for g(x) :

g o f (x) = g (f (x) )

= g (3x + 2)

= ((3x + 2) - 2)/3

= (3x)/3.

= x.

→ g o f (x) = x.

∴ f o g (x)  =  g o f (x) = x.

So, the given two functions are inverses of each other.

answered Jun 11, 2014 by lilly Expert

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