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


h(h(h(0)))

Verified step by step guidance

1. Identify the function h(x) from the given table.
2. Find the value of h(0) using the table.
3. Use the result from the previous step to find h(h(0)).
4. Use the result from the previous step to find h(h(h(0))).
5. Verify each step using the table to ensure accuracy.

Key Concepts

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.