Here are the essential concepts you must grasp in order to answer the question correctly.
Function Composition
Function composition involves combining two functions where the output of one function becomes the input of another. In this case, we need to evaluate g(f[h(1)]), which means we first find h(1), then use that result as the input for f, and finally use the output of f as the input for g.
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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 calculate the value of h at that point.
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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. When evaluating g(f[h(1)]), we must follow the correct order: first calculate h(1), then f of that result, and finally g of the output from f, ensuring accurate results.
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