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  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!
Finding the inverse of an equation algebraically. So for this particular example we have a function that is a cubic and we want to find its inverse. The first thing we always have to do before finding the inverse is to make sure is make sure it's 1 to 1 so we actually have an inverse.
Going with what we know for graphs this is just a transformation of a cubic graph. We know that this graph is standard normally something like this and the minus 2 just moves it over to the right 2 units. Horizontal line test tells us the original is a function we move it over it's still going to be a 1 to 1 function so therefore we know that this is going to have an inverse. So then we can go ahead and solve that algebraically.
So first thing we need to remember is f(x) is actually the same thing as y. So replace that with y and we end up a y equals equation. To find the inverse switch x and y. So x is equal to y minus 2 quantity cubed and then we solve for y to get rid of the power we need to take the cube root. We end up with the cube root of x is equal to y minus 2, solving for y add 2 to the other side, and then lastly replace our y with a function inverse notation, f inverse of x is equal to root three write the cube root of x plus 2.
So finding the inverse of a function make sure it's 1 to 1, replace f(x) with y switch x’s and y’s then solve for y.
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 5,977 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 3 704 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