Asked by nicole and brian!
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?
the question is y=3x-3...
we know how to make an inverse but how do you verify it using composition?
Answers
Answered by
Steve
one way is to check to make sure that
f(f<sup> -1</sup>(x)) = x
and
f<sup> -1</sup>(f(x)) = x
For example, if
f(x) = 2x-7
then solve for x to get f<sup> -1</sup>
y = 2x-7
(y+7)/2 = x
so, f<sup> -1</sup>(x) = (x+7)/2
Now,
f<sup> -1</sup>(f(x)) = (f(x)+7)/2
= ((2x-7)+7)/2
= (2x)/2
= x
and
f(f<sup> -1</sup>(x)) = 2f<sup> -1</sup>(x) - 7
= 2*(x+7)/2 - 7
= x+7-7
= x
Using values, just plug 'em in:
f(3) = 6-7 = -1
f<sup> -1</sup>(-1) = (-1+7)/2 = 3
f(f<sup> -1</sup>(x)) = x
and
f<sup> -1</sup>(f(x)) = x
For example, if
f(x) = 2x-7
then solve for x to get f<sup> -1</sup>
y = 2x-7
(y+7)/2 = x
so, f<sup> -1</sup>(x) = (x+7)/2
Now,
f<sup> -1</sup>(f(x)) = (f(x)+7)/2
= ((2x-7)+7)/2
= (2x)/2
= x
and
f(f<sup> -1</sup>(x)) = 2f<sup> -1</sup>(x) - 7
= 2*(x+7)/2 - 7
= x+7-7
= x
Using values, just plug 'em in:
f(3) = 6-7 = -1
f<sup> -1</sup>(-1) = (-1+7)/2 = 3