Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(-7/3)

Verified step by step guidance

1. Identify the function ƒ(x) given as ƒ(x) = -3x + 4.
2. Substitute the value x = -\frac{7}{3} into the function ƒ(x). This means replacing every x in the expression with -\frac{7}{3}.
3. Write the substitution explicitly: ƒ\left(-\frac{7}{3}\right) = -3 \times \left(-\frac{7}{3}\right) + 4.
4. Simplify the multiplication part: multiply -3 by -\frac{7}{3}.
5. After simplifying the multiplication, add 4 to the result to get the simplified expression for ƒ\left(-\frac{7}{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(-7/3), replace x with -7/3 in ƒ(x) and simplify the expression.

Linear Functions

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

Simplifying Algebraic Expressions

Simplifying involves performing arithmetic operations and reducing expressions to their simplest form. This is essential after substituting values into functions to present the final answer clearly and accurately.