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

Verified step by step guidance

1. Identify the given functions: \(f(x) = -3x + 4\) and \(g(x) = -x^2 + 4x + 1\).
2. To find \(f(a+4)\), substitute the expression \(a+4\) into the function \(f(x)\) wherever you see \(x\).
3. Write the substitution explicitly: \(f(a+4) = -3(a+4) + 4\).
4. Apply the distributive property to multiply \(-3\) by both \(a\) and \$4\(: \)-3 \times a\( and \)-3 \times 4$.
5. Simplify the expression by combining like terms to get the final form of \(f(a+4)\).

Key Concepts

Function Notation and Evaluation

Function notation, such as ƒ(x), represents a rule that assigns each input x to an output. Evaluating a function at a specific input means substituting that input into the function's formula and simplifying the result.

Substitution in Functions

Substitution involves replacing the variable in a function with a given expression or value. For example, to find ƒ(a+4), replace every x in ƒ(x) with (a+4) and simplify the resulting expression.

Simplifying Algebraic Expressions

Simplifying expressions means combining like terms and performing arithmetic operations to write the expression in its simplest form. This step is essential after substitution to present the final answer clearly.