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

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Identify the given functions: \(f(x) = -3x + 4\) and \(g(x) = -x^2 + 4x + 1\).

To find \(f(-x)\), substitute \(-x\) in place of \(x\) in the function \(f(x)\).

Write the substitution explicitly: \(f(-x) = -3(-x) + 4\).

Simplify the expression by multiplying: \(-3(-x) = 3x\).

Combine the terms to get the simplified form of \(f(-x)\): \(f(-x) = 3x + 4\).

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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 ƒ(x). Evaluating a function at a specific value means substituting that value into the function's formula and simplifying the result.

Substitution of Expressions into Functions

Substituting an expression like -x into a function involves replacing every instance of the variable x with the expression -x. This requires careful algebraic manipulation to simplify the resulting expression correctly.

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms, applying arithmetic operations, and reducing the expression to its simplest form. This step ensures the final answer is clear and concise.

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