For the pair of functions defined, find (f/g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-8

Key Concepts

Function Division

Function division involves creating a new function by dividing one function by another. In this case, (f/g)(x) is defined as f(x) divided by g(x), which means you will compute (3x + 4) / (2x - 8). Understanding how to manipulate and simplify rational functions is crucial for solving such problems.

Domain of a Function

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For the function (f/g)(x), the domain must exclude any values that make the denominator zero, as division by zero is undefined. In this case, you need to find the value of x that makes g(x) = 0.

Rational Functions

Rational functions are functions that can be expressed as the ratio of two polynomials. They often exhibit specific behaviors, such as asymptotes and discontinuities, based on the values of the numerator and denominator. Understanding the characteristics of rational functions helps in analyzing their graphs and determining their domains.