Problem 5
Question
Find the domain of each rational function. $$h(x)=\frac{x+7}{x^{2}-49}$$
Step-by-Step Solution
Verified Answer
The domain of the function is all real numbers except 7 and -7. So, \(x \in R, x \neq 7, -7\).
1Step 1: Set the denominator equal to zero
The first step is to set the denominator equal to zero, so \(x^{2}-49 = 0\). This is because we want to find the values of x which make the denominator zero so we can exclude them from the domain.
2Step 2: Solve for x
You can solve this equation by taking the square root of both sides to get \(x = \sqrt{49} = 7\) and \(x = -\sqrt{49} = -7\). So, x = 7 and x = -7 are the values that make the denominator zero.
3Step 3: Exclude the values from the domain
The domain of the function is all real numbers except the ones that make the denominator zero. So the values 7 and -7 need be excluded from the domain. This can be written as \(x \in R, x \neq 7, -7\)
Other exercises in this chapter
Problem 5
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 5
Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies directly as \(x\) and inversely as the square of \(z . y=20\
View solution Problem 5
In Exercises \(1-8,\) use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)-4 x^{4}-x^{3}+5 x^{2}-2 x-6 $$
View solution Problem 5
Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$ \left(6 x^{3}+7 x^{2}+12 x-5\right) \div(3 x-1) $$
View solution