Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. g(-2)

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Identify the function g(x) given as \(g(x) = -x^{2} + 4x + 1\).

To find \(g(-2)\), substitute \(x = -2\) into the function \(g(x)\).

Replace every \(x\) in the expression with \(-2\): \(g(-2) = -(-2)^{2} + 4(-2) + 1\).

Simplify the expression step-by-step: first calculate \((-2)^{2}\), then multiply by the coefficients, and finally add all terms.

Write the simplified expression after substitution to get the value of \(g(-2)\) (do not calculate the final numeric value here).

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Key Concepts

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

Function Evaluation

Function evaluation involves substituting a given input value into the function's formula and simplifying to find the output. For example, to find g(-2), replace every x in g(x) with -2 and simplify the expression.

Polynomial Functions

Polynomial functions are expressions involving variables raised to whole number powers combined using addition, subtraction, and multiplication. Understanding how to handle terms like -x² and 4x is essential for correctly evaluating and simplifying the function.

Order of Operations

The order of operations (PEMDAS) dictates the sequence to simplify expressions: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Correctly applying this ensures accurate evaluation of functions, especially when dealing with powers and multiple terms.

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