Use the table to evaluate the given compositions.

Question

h(h(h(0)))

Accepted Answer

Welcome back everyone. In this problem, we want to provide the value of the composite function k of k of k of negative one based on the table below. For our answer choices, a is 0, b is 2, c is 4, and d is 6. Now what do we know? We want to get the value of the composite function. And a function is a composite function when we're putting one function into another. Recall that to determine the value of a composite function, we evaluate the innermost function first and then work our way outward. So let's see if we can do that with the help of our table. So evaluating our innermost function first. K. It means that for our composite function, k of k of k of negative one, we're going to start by evaluating k of negative one. Now k of negative one means that we're finding the value of k when x equals negative one. And when x equals negative one, k equals 0. So k of negative one is actually equal to 0. Now, we're not done yet. So let me put that in red. K. 0. We're not done yet because we still need to find the k of 0. So we evaluate our innermost function again. So we need to figure out what k of 0 is. K of 0 means we want the value of k when x equals 0. And when x equals 0, k equals 2. So now we can rewrite our function as k of 2. And I'll put that in purple to show that k of 0 equals 2. Now we're almost there because we just need to find the value of k of 2. When x equals 2, k is 6. So therefore, our original expression, k of k of k of negative one eventually equals to 6. When we look back in our answer choices, that would have been answer choice d. Thanks a lot for watching everyone. I hope this video helped.

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

h(h(h(0)))

Key Concepts

Function Composition

Evaluating Functions

Iterated Functions

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