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Questions: Algebra BusinessCalculus
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If \(\displaystyle f(x)=- \frac{7}{3 - 6 x}\) and \(\displaystyle g(x)=7 x^{3} + x^{2} - 3 x + 9\) find \(\displaystyle (f\circ g)(x)\).
Evaluating \(\displaystyle f(x)\) at \(\displaystyle g(x)\) gives \(\displaystyle (f\circ g)(x)=f(g(x))=- \frac{7}{- 42 x^{3} - 6 x^{2} + 18 x - 51}\).
\begin{question}If $f(x)=- \frac{7}{3 - 6 x}$ and $g(x)=7 x^{3} + x^{2} - 3 x + 9$ find $(f\circ g)(x)$.
\soln{9cm}{Evaluating $f(x)$ at $g(x)$ gives $(f\circ g)(x)=f(g(x))=- \frac{7}{- 42 x^{3} - 6 x^{2} + 18 x - 51}$. }
\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>If <img class="equation_image" title=" \displaystyle f(x)=- \frac{7}{3 - 6 x} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%3D-%20%5Cfrac%7B7%7D%7B3%20-%206%20x%7D%20" alt="LaTeX: \displaystyle f(x)=- \frac{7}{3 - 6 x} " data-equation-content=" \displaystyle f(x)=- \frac{7}{3 - 6 x} " /> and <img class="equation_image" title=" \displaystyle g(x)=7 x^{3} + x^{2} - 3 x + 9 " src="/equation_images/%20%5Cdisplaystyle%20g%28x%29%3D7%20x%5E%7B3%7D%20%2B%20x%5E%7B2%7D%20-%203%20x%20%2B%209%20" alt="LaTeX: \displaystyle g(x)=7 x^{3} + x^{2} - 3 x + 9 " data-equation-content=" \displaystyle g(x)=7 x^{3} + x^{2} - 3 x + 9 " /> find <img class="equation_image" title=" \displaystyle (f\circ g)(x) " src="/equation_images/%20%5Cdisplaystyle%20%28f%5Ccirc%20g%29%28x%29%20" alt="LaTeX: \displaystyle (f\circ g)(x) " data-equation-content=" \displaystyle (f\circ g)(x) " /> . </p> </p><p> <p>Evaluating <img class="equation_image" title=" \displaystyle f(x) " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20" alt="LaTeX: \displaystyle f(x) " data-equation-content=" \displaystyle f(x) " /> at <img class="equation_image" title=" \displaystyle g(x) " src="/equation_images/%20%5Cdisplaystyle%20g%28x%29%20" alt="LaTeX: \displaystyle g(x) " data-equation-content=" \displaystyle g(x) " /> gives <img class="equation_image" title=" \displaystyle (f\circ g)(x)=f(g(x))=- \frac{7}{- 42 x^{3} - 6 x^{2} + 18 x - 51} " src="/equation_images/%20%5Cdisplaystyle%20%28f%5Ccirc%20g%29%28x%29%3Df%28g%28x%29%29%3D-%20%5Cfrac%7B7%7D%7B-%2042%20x%5E%7B3%7D%20-%206%20x%5E%7B2%7D%20%2B%2018%20x%20-%2051%7D%20" alt="LaTeX: \displaystyle (f\circ g)(x)=f(g(x))=- \frac{7}{- 42 x^{3} - 6 x^{2} + 18 x - 51} " data-equation-content=" \displaystyle (f\circ g)(x)=f(g(x))=- \frac{7}{- 42 x^{3} - 6 x^{2} + 18 x - 51} " /> . </p> </p>