Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. ƒ(0)

Verified step by step guidance

1. Identify the function ƒ(x) given as ƒ(x) = -3x + 4.
2. To find ƒ(0), substitute x = 0 into the function ƒ(x).
3. Write the substitution explicitly: ƒ(0) = -3(0) + 4.
4. Simplify the expression by multiplying and adding the terms.
5. The result after simplification will be the value of ƒ(0).

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into the function's formula to find the corresponding output. For example, to find ƒ(0), replace x with 0 in ƒ(x) and simplify the expression.

Linear Functions

A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept. Understanding this helps in quickly evaluating and interpreting the function's behavior for given inputs.

Simplification of Algebraic Expressions

Simplification involves performing arithmetic operations and combining like terms to write expressions in their simplest form. This is essential after substituting values to present the final answer clearly.