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Home Question Bank Math Pre Calculus Archive 2024 November 03

Pre-calculus Questions from Nov 03,2024

Browse the Pre-calculus Q&A Archive for Nov 03,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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En las siguientes funciones biyectivas, defina sus funciones inversas: (a) \( f:]-\infty, 7] \rightarrow\left[0,+\infty\left[\right.\right. \) tal que \( f(x)=\sqrt{1-\frac{x-2}{5}} \) (9) Senala el rango de la función: \( y=f(x)=3+4 \cos x ; \) Df: \( R \) \( \begin{array}{ll}\text { a) }[3 ; 4] & \text { d) }[\square 1 ; 7] \\ \text { b) }[1 ; 4] & \text { e) }[\square 1 ; 3] \\ \text { c) }[1 ; 4] & \end{array} \) Find the domain of \( f \) \[ \begin{array}{l}f(x)=\frac{\sqrt{5 x-8}}{x^{2}-13 x+12} \\ (-\infty, 12) \cup(12, \infty) \\ (-8,-5) \cup(12,13) \\ {\left[-\frac{5}{8}, 12\right) \cup(13, \infty)} \\ {\left[\frac{8}{5}, 12\right) \cup(12, \infty)} \\ \left(-\infty, \frac{8}{5}\right) \cup(12, \infty)\end{array} \] Señala el dominio de la función: \( f(x)=\frac{\operatorname{sen} x+2}{\cos x+1} \) a) \( R \square\{n \pi ; n \in Z\} \) b) \( R \square\{n \pi / 2 ; n \in Z\} \) c) \( R \square\{(2 n+1) \pi / 2 ; n \in Z\} \) d) \( R \square\{2 n \pi ; n \in Z\} \) e) \( R \square\{(2 n+1) \pi ; n \in Z\} \) Find the domain of \( f \) \[ \begin{array}{l}f(x)=\frac{5 x}{8 x^{2}+10 x-3} \\ \mathbb{R}_{\mathbb{R}}-\left\{-\frac{1}{4}\right\} \\ \mathbb{R}_{\mathbb{R}} \\ \mathbb{R}_{\mathbb{R}}-\left\{-\frac{3}{2}, \frac{1}{4}, 0\right\} \\ \mathbb{R}_{\mathbb{R}}^{2},\left\{-\frac{3}{2}\right\}\end{array} \] \( f(x) \) is a rational function given in both standard and factored forms. Let \( f(x)=\frac{15 x^{2}+34 x-16}{8 x^{2}-10 x-3}=\frac{(5 x-2)(3 x+8)}{(4 x+1)(2 x-3)} \) Find: Horizontal as, \( f(x) \) is a rational function given in both standard and factored forms. Let \( f(x)=\frac{x-4}{x^{2}-2 x-8}=\frac{(x-4)}{(x+2)(x-4)} \) Find: Vertical asymptotes at \( x=\square \) \( - 1 \leq \frac { \alpha \gamma + \beta \delta } { \sqrt { \alpha ^ { 2 } + \beta ^ { 2 } } \sqrt { \gamma ^ { 2 } + \delta ^ { 2 } } } \leq 1 \) Which of these shows the graph of \( f(x)=-\frac{1}{2} \cos \left(\frac{1}{3} x\right) \) ? 5. Determina, en cada cas atniba o hacia abajo. a. \( f(x)=-5 x+3 x^{2} \)
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