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Questions: Algebra BusinessCalculus
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Find the domain of \(\displaystyle f(x) = \sqrt{20 - 2 x} + 4\). Write the solution in interval notation.
The domain of a radical function is the solution to the inequality radicand \(\displaystyle \geq 0\). The inequality is \(\displaystyle 20 - 2 x \geq 0\). Isolating \(\displaystyle x\) gives \(\displaystyle - 2 x \geq -20\) Dividing to finish isolating \(\displaystyle x\) gives \(\displaystyle x \leq 10\). The domain is \(\displaystyle \left(-\infty, 10\right]\)
\begin{question}Find the domain of $f(x) = \sqrt{20 - 2 x} + 4$. Write the solution in interval notation.
\soln{9cm}{The domain of a radical function is the solution to the inequality radicand $\geq 0$. The inequality is $20 - 2 x \geq 0$. Isolating $x$ gives $- 2 x \geq -20$ Dividing to finish isolating $x$ gives $x \leq 10$. The domain is $\left(-\infty, 10\right]$}
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Find the domain of <img class="equation_image" title=" \displaystyle f(x) = \sqrt{20 - 2 x} + 4 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20%5Csqrt%7B20%20-%202%20x%7D%20%2B%204%20" alt="LaTeX: \displaystyle f(x) = \sqrt{20 - 2 x} + 4 " data-equation-content=" \displaystyle f(x) = \sqrt{20 - 2 x} + 4 " /> . Write the solution in interval notation. </p> </p><p> <p>The domain of a radical function is the solution to the inequality radicand <img class="equation_image" title=" \displaystyle \geq 0 " src="/equation_images/%20%5Cdisplaystyle%20%5Cgeq%200%20" alt="LaTeX: \displaystyle \geq 0 " data-equation-content=" \displaystyle \geq 0 " /> . The inequality is <img class="equation_image" title=" \displaystyle 20 - 2 x \geq 0 " src="/equation_images/%20%5Cdisplaystyle%2020%20-%202%20x%20%5Cgeq%200%20" alt="LaTeX: \displaystyle 20 - 2 x \geq 0 " data-equation-content=" \displaystyle 20 - 2 x \geq 0 " /> . Isolating <img class="equation_image" title=" \displaystyle x " src="/equation_images/%20%5Cdisplaystyle%20x%20" alt="LaTeX: \displaystyle x " data-equation-content=" \displaystyle x " /> gives <img class="equation_image" title=" \displaystyle - 2 x \geq -20 " src="/equation_images/%20%5Cdisplaystyle%20-%202%20x%20%5Cgeq%20-20%20" alt="LaTeX: \displaystyle - 2 x \geq -20 " data-equation-content=" \displaystyle - 2 x \geq -20 " /> Dividing to finish isolating <img class="equation_image" title=" \displaystyle x " src="/equation_images/%20%5Cdisplaystyle%20x%20" alt="LaTeX: \displaystyle x " data-equation-content=" \displaystyle x " /> gives <img class="equation_image" title=" \displaystyle x \leq 10 " src="/equation_images/%20%5Cdisplaystyle%20x%20%5Cleq%2010%20" alt="LaTeX: \displaystyle x \leq 10 " data-equation-content=" \displaystyle x \leq 10 " /> . The domain is <img class="equation_image" title=" \displaystyle \left(-\infty, 10\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%28-%5Cinfty%2C%2010%5Cright%5D%20" alt="LaTeX: \displaystyle \left(-\infty, 10\right] " data-equation-content=" \displaystyle \left(-\infty, 10\right] " /> </p> </p>