Table of contents
- 0. Functions7h 52m
- Introduction to Functions16m
- Piecewise Functions10m
- Properties of Functions9m
- Common Functions1h 8m
- Transformations5m
- Combining Functions27m
- Exponent rules32m
- Exponential Functions28m
- Logarithmic Functions24m
- Properties of Logarithms34m
- Exponential & Logarithmic Equations35m
- Introduction to Trigonometric Functions38m
- Graphs of Trigonometric Functions44m
- Trigonometric Identities47m
- Inverse Trigonometric Functions48m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation3h 18m
- 4. Applications of Derivatives2h 38m
- 5. Graphical Applications of Derivatives6h 2m
- 6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
- 7. Antiderivatives & Indefinite Integrals1h 26m
0. Functions
Common Functions
Problem 1.R.17
Textbook Question
Assume f is an odd function and that both f and g are one-to-one. Use the (incomplete) graph of f and the graph of g to find the following function values. <IMAGE>
f-1(1 + f(-3))
![](/channels/images/assetPage/verifiedSolution.png)
1
Step 1: Understand the properties of odd functions. An odd function satisfies the condition f(-x) = -f(x) for all x in the domain of f.
Step 2: Use the property of odd functions to find f(-3). Since f is odd, f(-3) = -f(3).
Step 3: Calculate 1 + f(-3) using the result from Step 2. This becomes 1 - f(3).
Step 4: Understand the property of one-to-one functions. A function is one-to-one if it has an inverse, meaning each output is mapped from a unique input.
Step 5: Use the inverse function property to find f^{-1}(1 + f(-3)). Since 1 + f(-3) = 1 - f(3), find the x such that f(x) = 1 - f(3).
Recommended similar problem, with video answer:
![](/channels/images/assetPage/verifiedSolution.png)
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
4mPlay a video:
Was this helpful?
Watch next
Master Graphs of Common Functions with a bite sized video explanation from Nick
Start learningRelated Videos
Related Practice