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

Verified step by step guidance

1. Identify the function ƒ(x) given as ƒ(x) = -3x + 4.
2. To find ƒ(1/3), substitute x = \frac{1}{3} into the function ƒ(x).
3. Write the substitution explicitly: ƒ\left(\frac{1}{3}\right) = -3 \times \frac{1}{3} + 4.
4. Multiply -3 by \frac{1}{3} to simplify the expression inside the function.
5. Add the result of the multiplication to 4 to get the simplified value of ƒ\left(\frac{1}{3}\right).

Key Concepts

Function Evaluation

Function evaluation involves substituting a given input value into the function's formula and simplifying to find the output. For example, to find ƒ(1/3), replace x with 1/3 in ƒ(x) and simplify the expression.

Linear Functions

A linear function has the form ƒ(x) = mx + b, where m and b are constants. Its graph is a straight line, and evaluating it involves simple arithmetic operations like multiplication and addition.

Simplification of Algebraic Expressions

Simplification means reducing an expression to its simplest form by performing arithmetic operations and combining like terms. This step ensures the final answer is clear and concise.