Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. g(10)

Verified step by step guidance

1. Identify the function g(x) given as \(g(x) = -x^2 + 4x + 1\).
2. To find \(g(10)\), substitute \(x = 10\) into the function \(g(x)\).
3. Replace every \(x\) in the expression with 10: \(g(10) = -(10)^2 + 4(10) + 1\).
4. Simplify the expression step-by-step: first calculate \$10^2$, then multiply and add the terms accordingly.
5. Write the simplified expression after performing the arithmetic operations to get the value of \(g(10)\).

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(10), replace x with 10 in g(x) and simplify the expression to get the output.

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.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses, exponents, multiplication/division, and addition/subtraction (PEMDAS). Correctly applying this order ensures accurate evaluation of functions, especially when dealing with powers and multiple terms.