Questions: R(x)=3/(x-2)(x+2) (Type your answer in factored form. Do not simplify) R(x) is already in factored form What is the domain of R(x)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ) (Type an integer or a simplified fraction) B. x x ? (Type an integer or a simplified fraction) D. The domain is the set of all real numbers.

R(x)=3/(x-2)(x+2) (Type your answer in factored form. Do not simplify) R(x) is already in factored form What is the domain of R(x)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ) (Type an integer or a simplified fraction) B. x x ? (Type an integer or a simplified fraction) D. The domain is the set of all real numbers.
Transcript text: VA. $R(x)=\frac{3}{(x-2)(x+2)}$ (Type your answer in factored form. Do not simplify) B. $R(x)$ is already in factored form What is the domain of $R(x)$? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. $\square$ ) (Type an integer or a simplified fraction) B. $\{x \mid x\}$ $\square$ $\square$ ? (Type an integer or a simplified fraction) D. The domain is the set of all real numbers.
failed

Solution

failed
failed

Solution Steps

To determine the domain of the rational function \( R(x) = \frac{3}{(x-2)(x+2)} \), we need to identify the values of \( x \) that make the denominator zero, as these are the values that are not included in the domain. The domain will be all real numbers except these values.

Step 1: Identify the Denominator

The function is given by

\[ R(x) = \frac{3}{(x-2)(x+2)} \]

To find the domain, we need to analyze the denominator, which is

\[ (x-2)(x+2). \]

Step 2: Solve for Excluded Values

We set the denominator equal to zero to find the values of \( x \) that are not allowed in the domain:

\[ (x-2)(x+2) = 0. \]

This gives us the solutions:

\[ x - 2 = 0 \quad \Rightarrow \quad x = 2, \] \[ x + 2 = 0 \quad \Rightarrow \quad x = -2. \]

Step 3: State the Domain

The domain of \( R(x) \) is all real numbers except the values that make the denominator zero. Therefore, the domain can be expressed as:

\[ \text{Domain} = \mathbb{R} \setminus \{-2, 2\}. \]

Final Answer

The domain of \( R(x) \) is

\[ \boxed{\mathbb{R} \setminus \{-2, 2\}}. \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
37 = 111 - x x =
failedAnswered
The names and chemical formulae of some chemical compounds are written in the first two columns of the table below. Each compound is soluble in water. Imagine that a few tenths of a mole of each compound is dissolved in a liter of water. Then, write down in the third column of the table the chemical formula of the major chemical species that will be present in this solution. For example, you know water itself will be present, so you can begin each list with the chemical formula for water (H2O). Note: "major" chemical species are those present in concentrations greater than 10^-6 mol / L. compound formula major species present when dissolved in water --------- methanol CH3OH propylene glycol C3H6(OH)2 glycerol C3H8O3
failedAnswered
Reparametrize the curve with respect to arc length measured from the point where t=0 in the direction of increasing t. (Enter your answer in terms of s.) r(t)=e^(6t) cos(6t) i+6 j+e^(6t) sin(6t) k r(t(s))=
failedAnswered
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. I'm putting all my savings into stocks because stocks always outperform other types of investments over the long term. Choose the correct answer below. A. The statement does not make sense because although stocks historically outperform bonds and cash over the long term, investing in stocks is high-risk and there is no guarantee that the investment will yield a high return. B. The statement does make sense because stocks are a low-risk investment, offering predictable low returns. C. The statement does make sense because stocks historically outperform bonds and cash over the long term and investing in stocks is high-risk, which offers higher returns. D. The statement does not make sense because stocks never outperform bonds and cash over the long term.
failedAnswered
Determine the net income of a company for which the following information is available for the month of September. Service revenue 320,000 Rent expense 58,000 Utilities expense 4,200 Salaries expense 91,000