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
Finding an Inverse Algebraically  Concept
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!
Once we learn the definition of a function's inverse we learn how to find the algebraic inverse, or how to find the inverse using algebraic methods. There are different methods for finding the inverse, the most common of which is to switch the dependent and independent variables and solve for the dependent variable. This is an important step in learning how to prove the inverse of a function.
Finding the inverse of a funtion Algebraically. So for this particular example, so what we want to do is find an equation for a inverse function. We're given a function here. In this case we know that our equation is a line. 3x2 we know that's a line therefore we know it's 1 to 1 and it's going to have an inverse.
So how we find a inverse is by switching our x and our y, for this particular problem we don't have a y but what we need to remember is f of x is the same thing as y. So just by replacing f of x with y, 3x2, I now have an equation using x and y. To find the inverse we switch x and y's, okay? So every time we see an x, we throw in a y, every time we see a y we throw in an x. Okay? And we're used to seeing equations of y equals. So really from here all we want to do is solve for y. Okay?
So do that as we would any other equqtion, add 2 to both sides x+2=3y divided by 3, x+2 divide by 3 is equal to y. And then we found y but we're asked to find f inverse of x. Once we switch our variables solve for y, this is now the inverse okay? So we can replace our y with our inverse notation. x+2 over 3. Okay?
So to find the inverse, it's quite simple. So make sure you if you have an f of x replace it with y. solve through sorry. Switch your x and y's. Solve through for y making sure to replace it with your inverse notation at the end.
Now some teachers do this a little different and I just want to touch on that for a second. You don't have to switch x and y right here, okay? What you could do is actually solve for this x and then switch it. In general, I tend to shy away from that just because I'm so used to solving for y where what I've done is I've done problems where I haven't switched it. Halfway down the problem I forget that I'm solving for x, go back solve for y and I end up with exactly what I started with. Okay?
But if you can keep track what you're solving for, that's perfectly acceptable. For me, I always switch it. Fairly one of my first steps solve for y and then just make sure you replace your inverse notation.
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”
Get Peer Support on User Forum
Peer helping is a great way to learn. Join your peers to ask & answer questions and share ideas.
Concept (1)
Sample Problems (10)
Need help with a problem?
Watch expert teachers solve similar problems.

Finding an Inverse Algebraically
Problem 1 5,978 viewsFind f⁻¹(x) given
f(x) = (x − 2)³ 
Finding an Inverse Algebraically
Problem 2 4,661 viewsFind g⁻¹(x) given
g(x) = x² + 2 
Finding an Inverse Algebraically
Problem 3 705 views 
Finding an Inverse Algebraically
Problem 4 559 views 
Finding an Inverse Algebraically
Problem 5 564 views 
Finding an Inverse Algebraically
Problem 6 539 views 
Finding an Inverse Algebraically
Problem 7 502 views 
Finding an Inverse Algebraically
Problem 8 492 views 
Finding an Inverse Algebraically
Problem 9 628 views 
Finding an Inverse Algebraically
Problem 10 562 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete