algebra II
posted by nicole and brian! on .
How do you verify inverses?
the question is y=3x3...
we know how to make an inverse but how do you verify it using composition?

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) = 2x7
then solve for x to get f^{ 1}
y = 2x7
(y+7)/2 = x
so, f^{ 1}(x) = (x+7)/2
Now,
f^{ 1}(f(x)) = (f(x)+7)/2
= ((2x7)+7)/2
= (2x)/2
= x
and
f(f^{ 1}(x)) = 2f^{ 1}(x)  7
= 2*(x+7)/2  7
= x+77
= x
Using values, just plug 'em in:
f(3) = 67 = 1
f^{ 1}(1) = (1+7)/2 = 3