Table of contents

0. Functions7h 52m
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
8. Definite Integrals4h 44m
9. Graphical Applications of Integrals2h 27m
- Area Between Curves
  1h 18m
- Introduction to Volume & Disk Method
  1h 8m
10. Physics Applications of Integrals 3h 16m
- Kinematics
  1h 13m
- Work
  2h 3m
11. Integrals of Inverse, Exponential, & Logarithmic Functions2h 34m
12. Techniques of Integration7h 39m
13. Intro to Differential Equations2h 55m
14. Sequences & Series5h 36m
15. Power Series2h 19m
- Introduction to Power Series
  1h 9m
- Taylor Series & Taylor Polynomials
  1h 10m
16. Parametric Equations & Polar Coordinates7h 58m

0. Functions

Combining Functions

Calculus

0. Functions

Combining Functions

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2:30 minutes

Problem 16f

Textbook Question

Use the table to evaluate the given compositions. <IMAGE>

h(h(h(0)))

Verified step by step guidance

Identify the function h(x) from the given table.

Find the value of h(0) using the table.

Use the result from the previous step to find h(h(0)).

Use the result from the previous step to find h(h(h(0))).

Verify each step using the table to ensure accuracy.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Composition

Function composition involves combining two or more functions to create a new function. If you have functions f(x) and g(x), the composition f(g(x)) means you apply g first and then apply f to the result. Understanding how to evaluate compositions is crucial for solving problems that involve multiple functions.

Evaluating Functions

Evaluating a function means substituting a specific input value into the function to find the output. For example, if h(x) is a function, then h(0) means you replace x with 0 in the function h. This process is essential for determining the values needed when working with function compositions.

Iterated Functions

Iterated functions refer to applying a function multiple times in succession. In the expression h(h(h(0))), the function h is applied three times, starting with the input 0. Understanding how to iterate functions is important for evaluating complex compositions and determining the final output.