Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. 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. Simplify the expression step-by-step: first calculate \((-2)^2\), then multiply by the coefficients, and finally add all terms.
5. Write the simplified expression after performing all arithmetic operations to 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, such as squaring terms and combining like terms, is essential for simplifying expressions like g(x) = -x² + 4x + 1.

Simplification of Algebraic Expressions

Simplification means reducing an expression to its simplest form by performing arithmetic operations and combining like terms. After substituting values into functions, simplifying ensures the final answer is clear and concise.