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

Verified step by step guidance

1. Identify the function g(x) given as \(g(x) = -x^2 + 4x + 1\).
2. To find \(g(-2)\), substitute \(x = -2\) into the function \(g(x)\).
3. Replace every \(x\) in the expression with \(-2\): \(g(-2) = -(-2)^2 + 4(-2) + 1\).
4. Calculate each term step-by-step: first compute \((-2)^2\), then multiply by \(-1\), then multiply \$4\( by \)-2\(, and finally add \)1$.
5. Combine all the results to simplify the expression and find the value of \(g(-2)\).

Key Concepts

Function Evaluation

Function evaluation involves substituting a given input value into the function's formula and calculating the result. 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 exponents combined using addition, subtraction, and multiplication. Understanding how to work with polynomials, like g(x) = -x² + 4x + 1, is essential for evaluating and simplifying expressions.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses, exponents, multiplication/division, and addition/subtraction. Correctly applying this order ensures accurate simplification when evaluating functions.