Sophia: Finding the Inverse of a Function of a Function: Lesson 5

Analyze functions by decomposing complex functions and composing simple functions. Through a detailed lesson plan, pupils learn the vocabulary and notation related to the composition of functions. Practice includes both evaluating and...

Starting from a brief look at functions and the mapping of domains to ranges, Sal starts with an intuitive sense of what a function inverse is. Using an example, he then shows how to find the inverse of a function and how the graph of...

Sal continues showing examples of finding the inverse of the function. Here, he shows a subtle but essential technique of taking the negative square root of each side of the equation when solving for the inverse because of the...

Finding the inverse of trigonometric ratios is not the same as finding the reciprocal. The presentation introduces how to find the angle of a right triangle given sides. Part of a larger playlist on geometry, the video uses the inverse...

Sal continues looking at function inverses in this video by showing two examples. In each example, he finds the inverse and shows the graph of both functions. His examples are with linear functions, but his first example shows a function...

Sal shows an example of finding the inverse of the parabola with a restricted domain. He alludes to a reason behind the restricted domain but leaves the listener to determine it.

Determine the equation to use in evaluating a piecewise function. Learners watch a video on evaluating a piecewise function. They confirm the equation to use based on the domain and then use substitution to find the value of the function...

Reverse the wrapping to get to the gift. Using the idea of unwrapping a gift, the lesson plan introduces the concept of inverses. Pupils first determine the order needed to evaluate a function at a point, then use the reverse to find the...

Define the terms domain, range, function, vertical limit test, and linear function notation with your class. They can then, graph several equations applying the vertical line test to determine which are and which are not functions, write...

Take your kids on a tour of graphing rational functions. Using this TI lesson, high schoolers identify the end behavior of their functions. They find the domain and range, describe end behavior, and look at asymptotes and restrictions of...