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Questions: Algebra BusinessCalculus
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Find the domain of \(\displaystyle f(x) = \sqrt{20 x - 12} + 13\). 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 \(\displaystyle 20 x - 12 \geq 0\). Isolating \(\displaystyle x\) gives \(\displaystyle 20 x \geq 12\) Dividing to finish isolating \(\displaystyle x\) gives \(\displaystyle x \geq \frac{3}{5}\). The domain is \(\displaystyle \left[\frac{3}{5}, \infty\right)\)
\begin{question}Find the domain of $f(x) = \sqrt{20 x - 12} + 13$. 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 $20 x - 12 \geq 0$. Isolating $x$ gives $20 x \geq 12$ Dividing to finish isolating $x$ gives $x \geq \frac{3}{5}$. The domain is $\left[\frac{3}{5}, \infty\right)$}
\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 x - 12} + 13 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20%5Csqrt%7B20%20x%20-%2012%7D%20%2B%2013%20" alt="LaTeX: \displaystyle f(x) = \sqrt{20 x - 12} + 13 " data-equation-content=" \displaystyle f(x) = \sqrt{20 x - 12} + 13 " /> . 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 x - 12 \geq 0 " src="/equation_images/%20%5Cdisplaystyle%2020%20x%20-%2012%20%5Cgeq%200%20" alt="LaTeX: \displaystyle 20 x - 12 \geq 0 " data-equation-content=" \displaystyle 20 x - 12 \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 20 x \geq 12 " src="/equation_images/%20%5Cdisplaystyle%2020%20x%20%5Cgeq%2012%20" alt="LaTeX: \displaystyle 20 x \geq 12 " data-equation-content=" \displaystyle 20 x \geq 12 " /> 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 \geq \frac{3}{5} " src="/equation_images/%20%5Cdisplaystyle%20x%20%5Cgeq%20%5Cfrac%7B3%7D%7B5%7D%20" alt="LaTeX: \displaystyle x \geq \frac{3}{5} " data-equation-content=" \displaystyle x \geq \frac{3}{5} " /> . The domain is <img class="equation_image" title=" \displaystyle \left[\frac{3}{5}, \infty\right) " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cfrac%7B3%7D%7B5%7D%2C%20%5Cinfty%5Cright%29%20" alt="LaTeX: \displaystyle \left[\frac{3}{5}, \infty\right) " data-equation-content=" \displaystyle \left[\frac{3}{5}, \infty\right) " /> </p> </p>