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. In this case, we evaluate f(g(h(1))) by first finding h(1), then using that result as the input for g, and finally using the output of g as the input for f. This process illustrates how the output of one function becomes the input for another.
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Evaluating Functions
Evaluating a function means substituting a specific value into the function's equation to find the output. For example, to evaluate h(1), we substitute 1 into the equation h(x) = x² + x + 2, which allows us to compute the value of the function at that point. This step is crucial for function composition.
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Order of Operations
The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed. In function composition, we must evaluate the innermost function first, followed by the next function, and so on. This ensures that we correctly compute the final output of the composed functions.
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