Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. 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. Multiply -3 by -\frac{7}{3} carefully, remembering that multiplying two negatives results in a positive.
5. After the multiplication, add 4 to the result to simplify the expression and find 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 and b are constants. Its graph is a straight line, and evaluating it involves simple arithmetic operations like multiplication and addition.

Simplifying Rational Expressions

When substituting fractions into functions, it's important to carefully perform arithmetic with rational numbers. Simplifying involves reducing fractions and combining terms to express the result in simplest form.