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)

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. For example, to find g(-2), you replace x in the function g(x) with -2, allowing you to calculate the corresponding output value. This process is fundamental in understanding how functions behave at different points.

Polynomial Functions

Polynomial functions are mathematical 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 has a degree of 2. Understanding the structure of polynomial functions is essential for evaluating them and analyzing their properties.

Simplification of Expressions

Simplification of expressions involves reducing mathematical expressions to their simplest form, making them easier to work with. This can include combining like terms, factoring, or reducing fractions. In the context of evaluating g(-2), simplifying the resulting expression helps clarify the final output and ensures accuracy in calculations.