Like what you saw?
Create FREE Account and:
 Watch all FREE content in 21 subjects(388 videos for 23 hours)
 FREE advice on how to get better grades at school from an expert
 Attend and watch FREE live webinar on useful topics
Proving Two Functions are Inverses  Problem 2
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Proving that functions are inverses algebraically, whenever we prove that functions are inverses algebraically what we have to do is prove that the composition of two functions in both directions come out with x.
So the way I have written our composition is f of g of x and g of f of x. But those two functions are pretty arbitrary. What we really could say is f of f inverse of x, f of inverse of f, basically two functions that are inverses can go in here, so f and g in this cases are inverses we could have done standard notation f and f inverse.
So for this particular example we are given two functions we want to prove that they are inverses. It doesn’t matter what order we do our compositions because we are going to have to do both of them. So for this one I’ll start out with f of f inverse of x. Taking f inverse and plugging into f, so we have 2, f inverse goes in for x 1/2 x plus 3 those are f inverse plus 3. And do I have an extra parenthesis there I do.
So we want to prove that this is equal to x, so combine like terms inside of our parenthesis we end up with 2 1/2x plus 6 distribute in that 2 through we end up with x plus 12.
So we found the composition of f and f inverse to be x plus 12. In order for these two functions to be inverses what we have is for them to be x. We found it not to be x, so because one of them fails by default neither of these can be an inverse. So we don’t even need to find the other order we know that right away that these two functions are actually not inverses. So we could go through f inverse of f but there’s really no point because this is already proving they're not an inverse. Composition of functions always check to see if you are dealing with inverses.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
i love you you are the best, ive spent 3 hours trying to understand probability and this is making sense now finally”
BRIGHTSTORM IS A REVOLUTION !!!”
because of you i ve got a 100/100 in my test thanks”
Concept (1)
Sample Problems (4)
Need help with a problem?
Watch expert teachers solve similar problems.

Proving Two Functions are Inverses
Problem 1 5,584 viewsProve f(x) = 6x − 3 and g(x) = ⅙(x + 3) are inverses.

Proving Two Functions are Inverses
Problem 2 3,740 viewsProve f(x) = 2(x + 3) and f⁻¹(x) = ½x + 3 are inverses.

Proving Two Functions are Inverses
Problem 3 742 views 
Proving Two Functions are Inverses
Problem 4 770 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete