Problem 3
Question
Find the domain of each rational function. $$ g(x)=\frac{3 x^{2}}{(x-5)(x+4)} $$
Step-by-Step Solution
Verified Answer
The domain of the given function, \( g(x)=\frac{3 x^{2}}{(x-5)(x+4)} \), is all real numbers except 5 and -4.
1Step 1: Identifying the Denominator
Identify the denominator of the given rational function. In this case, the denominator is \( (x-5)(x+4) \).
2Step 2: Setting the Denominator Equal to Zero
We set the denominator equal to zero to find the values that will make the function undefined. In this case, we set \( (x-5)(x+4) = 0 \).
3Step 3: Solving for x
Solving the equation \( (x-5)(x+4) = 0 \) gives x = 5 and x = -4.
4Step 4: Form the Domain
The domain of g(x) is all real numbers except the values that make the function undefined. So the domain of g(x) would be all real numbers except 5 and -4.
Other exercises in this chapter
Problem 2
In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=x^{3}+3 x^{2}-6 x-8 $$
View solution Problem 2
Determine which functions are polynomial functions. For those that are, identify the degree. \(f(x)=7 x^{2}+9 x^{4}\)
View solution Problem 3
To complete the square of \(x^{2}-5 x\), you add the number \(\underline{\quad}.\)
View solution Problem 3
Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ (x-7
View solution