Problem 8
Question
Find the domain of each rational function. $$ f(x)=\frac{x+8}{x^{2}+64} $$
Step-by-Step Solution
Verified Answer
The domain of the given function is all real numbers.
1Step 1: Analyze the denominator
Analyze the denominator and set it equal to zero to find values that would make it undefined. So, \(x^{2} + 64 = 0\).
2Step 2: Solve the equation
Solve the equation for \(x\). In this equation, there is no real root because there are no real numbers that, squared, can give a result of -64. When squared, a real number always gives a positive result or zero.
3Step 3: Determine the domain
As there are no real roots to make the denominator zero, the domain of the given function is all real numbers.
Other exercises in this chapter
Problem 7
In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=x^{5}-x^{4}-7 x^{3}+7 x^{2}-12 x-12 $$
View solution Problem 7
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=x^{\frac{1}{2}}-3 x^{2}+5$$
View solution Problem 8
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^{2
View solution Problem 8
Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 1–10. C varies jointly as \(A\) and \(T . C=175\) when \(A=2100\
View solution