Posted by **nicole and brian!** on Wednesday, February 15, 2012 at 8:54pm.

How do you verify inverses?

the question is y=3x-3...

we know how to make an inverse but how do you verify it using composition?

- algebra II -
**Steve**, Thursday, February 16, 2012 at 11:06am
one way is to check to make sure that

f(f^{ -1}(x)) = x

and

f^{ -1}(f(x)) = x

For example, if

f(x) = 2x-7

then solve for x to get f^{ -1}

y = 2x-7

(y+7)/2 = x

so, f^{ -1}(x) = (x+7)/2

Now,

f^{ -1}(f(x)) = (f(x)+7)/2

= ((2x-7)+7)/2

= (2x)/2

= x

and

f(f^{ -1}(x)) = 2f^{ -1}(x) - 7

= 2*(x+7)/2 - 7

= x+7-7

= x

Using values, just plug 'em in:

f(3) = 6-7 = -1

f^{ -1}(-1) = (-1+7)/2 = 3

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