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