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

Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 59

Chapter 3, Problem 59

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

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Notation and Evaluation

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

Polynomial Functions

Polynomial functions are expressions involving variables raised to whole-number exponents combined using addition, subtraction, and multiplication. Understanding the structure of linear (e.g., -3x + 4) and quadratic (e.g., -x² + 4x + 1) polynomials helps in evaluating and simplifying function expressions.

Simplification of Algebraic Expressions

Simplification involves combining like terms and performing arithmetic operations to write expressions in their simplest form. After substituting values into functions, simplifying ensures the final answer is clear and concise, which is essential for accurate interpretation.

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