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)

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value into a function to determine its output. For example, to find g(10), you replace x in the function g(x) with 10, allowing you to compute the value of the function at that point.

Polynomial Functions

Polynomial functions are expressions that involve variables raised to whole number powers, combined using addition, subtraction, and multiplication. In this case, g(x) = -x^2 + 4x + 1 is a quadratic polynomial, which can be analyzed for its properties such as roots and vertex.

Simplification of Expressions

Simplification of expressions involves reducing a mathematical expression to its simplest form. This can include combining like terms, factoring, or performing arithmetic operations to make the expression easier to understand or work with, which is essential when evaluating functions.