Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(p)

검증된 단계별 안내

Identify the function ƒ(x) given as ƒ(x) = -3x + 4.

To find ƒ(p), substitute the variable x in the function ƒ(x) with p.

Write the expression after substitution: ƒ(p) = -3p + 4.

Simplify the expression if possible. In this case, the expression is already simplified.

The final expression for ƒ(p) is -3p + 4.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Function Notation and Evaluation

Function notation, such as f(x), represents a rule that assigns each input x to an output f(x). Evaluating a function at a specific input, like f(p), means substituting the variable with the given value and simplifying the expression.

Polynomial Functions

Polynomial functions are expressions involving variables raised to whole number powers with coefficients. Understanding how to manipulate and simplify polynomials, such as linear (f(x) = -3x + 4) and quadratic (g(x) = -x² + 4x + 1), is essential for evaluating and combining functions.

Substitution Method

The substitution method involves replacing the variable in a function with a given value or expression. This technique is crucial for finding function values like f(p), where p is substituted into the function's formula to compute the result.