Learn math, science, English SAT & ACT from
highquaility study
videos by expert teachers
Thank you for watching the preview.
To unlock all 5,300 videos, start your free trial.
Proving Two Functions are Inverses  Problem 1
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 two functions are inverses algebraically. So if we want to prove that two functions are inverses what we have to do is a composition of the two of them in both orders and see that we get x out.
So for this example I have two different problems up here and I want to prove that they are inverses. So the first thing I want to look at is f of g of x which is telling me I’m taking g and I’m plugging it into f. So wherever I see an x and f in goes g. Oops that’s a minus, no that’s a plus I was right and then minus 3. So this one simplifies quite easily, multiplying by 6 dividing by 6, these are going to cancel, x plus 3 minus 3, our 3’s cancel just leaving me with x.
So I did one step, I did the composition of f and g I also need to do the opposite to make sure that the same thing x just comes out. So for this one g of f of x, now we are taking f and plugging it into g we end with, let’s try that again we are taking f plugging it in over there so we end up with 6x minus 3 plus 3 over 6 so there is our f function. So we have minus 3 plus 3, 3’s cancel 6 x over 6, 6’s cancel just leaving us with x.
So composition of f and g both orders x came out so we have in fact proved that they are inverses. So always make sure you do both orders because it is possible for one to come out x the other one not to which will tell us they are not an inverse.
So composition you know we in fact should go back and refresh how to do these compositions everything else should be pretty straight forward.
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.
Concept (1)
Sample Problems (4)
Need help with a problem?
Watch expert teachers solve similar problems.

Proving Two Functions are Inverses
Problem 1 6,797 viewsProve f(x) = 6x − 3 and g(x) = ⅙(x + 3) are inverses.

Proving Two Functions are Inverses
Problem 2 4,100 viewsProve f(x) = 2(x + 3) and f⁻¹(x) = ½x + 3 are inverses.

Proving Two Functions are Inverses
Problem 3 968 views 
Proving Two Functions are Inverses
Problem 4 1,002 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete