Learning Resources
Outcomes
By the end of this lesson you will be able to answer questions like the ones in the pre-test below.
Approach #1
Answer the questions on the pre-test below in your Math 3103 binder. Then refer to the pages of the lesson that contain instruction on the questions you were unable to do, for which you got an incorrect answer, or for which you would like some further explanation.
Approach #2
Proceed directly to the first page of the lesson without attempting the pre-test. To do this simply click on the Lesson button above. You can then return to this pre-test later and use it as a worksheet.
Pre-test
1(a) Explain in words and algebraically why f(x) = 2x and g(x) = 
x are inverse
functions.
(b) Sketch a mapping diagram with at least 3 values in the domain to illustrate
this.
2(a) Explain in words and algebraically why f(x) = x2 and g(x) = 
are not
inverse functions.
(b) Sketch a mapping diagram to illustrate this.
3. Sketch a graph of the inverse of each of the functions graphed below and tell whether the inverse is also a function.:
(a) 
(b) 
(c) 
4. (a) Sketch the graph of the inverse of the following function.
(b) Explain why the inverse is not a function.
(c) Suggest a test for the graph of a function to determine if it has an inverse which is also a function.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- The definition of a function.
- The definition of and how to find the domain and range of a function.
- The various methods of describing a function, viz. "f of x" notation, graphing, and mapping diagrams.
- How to find the value of f(x) for a given value of x.
- How to substitute one expression or formula into a second expression or formula.
- How to reflect a point in a line on the Cartesian coordinate plane.