Don't Stop Learning Now!
Gain access to 3,500 HD videos.
Find Study Help
Watch All Videos FREE for 1 Week
No credit card required.TRY 1 WEEK FREE
Definition of Inverse - Problem 3 136 views
We know that in order to find the inverse of a function algebraically, we need to swap x and y and then solve for y. In doing this, the domain and range get swapped, as well. We can see this graphically as a function and its inverse are reflected across the line y = x. When working with radical functions in particular, we need to make sure that whatever is under the radical, called the radicand, is always greater than or equal to zero. This will help us verify that the domain and range have been swapped. To check our work, we need to use composition of functions to show that f(f-1(x)) = f-1(f(x))= x .
Transcript Coming Soon!
Please enter your name.
Are you sure you want to delete this comment?
Sample Problems (5)
Need help with a problem?
Watch expert teachers solve similar problems.
- Definition of One-to-One Functions 16,277 views
- Finding an Inverse Algebraically 18,544 views
- Proving Two Functions are Inverses 13,814 views
- Finding an Inverse Graphically 15,358 views
- Exponential Functions and their Graphs 34,262 views
- Solving Exponential Equations with the 'Same' Base 23,789 views
- Introduction to Logarithms 28,606 views
- Solving Simple Logarithmic Equations 25,080 views
- Function Notation with Logs and Exponentials 13,017 views
- Graph of Logarithmic Functions 25,226 views
- Product Rule of Logarithms 14,544 views
- Quotient Rule of Logarithms 13,994 views
- Power Rule of Logarithms 18,284 views
- Expanding Logarithms 19,474 views
- Condensing Logarithms 23,638 views
- Common and Natural Logarithms 20,154 views
- Change of Base Formula 17,500 views
- Solving Exponential Equations with the Different Bases 60,078 views
- Solving a Logarithmic Equation 23,727 views
- Solving a Logarithmic Equation with Multiple Logs 20,860 views
- Compound Interest (Finite Number of Calculations) 15,929 views
- Compound Interest (Continuously) 15,820 views
- Exponential Growth and Decay 17,593 views
- Evaluating a Logarithmic Expression in terms of Known Quantities 13,748 views