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

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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 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.

Recommended video: