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Home Question Bank Math Pre Calculus Archive 2024 November 10

Pre-calculus Questions from Nov 10,2024

Browse the Pre-calculus Q&A Archive for Nov 10,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Найдите область определения функции: \( f(x)=\frac{\sqrt{x^{2}+7}}{(11+5 x) \cdot \sqrt{2-6 x}} \). Запишите ответ в виде промежутка (объединения промежутков). \[ f(x)=\frac{\arccos \left(\ln x^{2}\right)}{x^{2}+1} \] fonksiyonunun tanım kümesi aşağıdakilerden hangisidir? 4. Найдите область определения функции \( y=\sqrt[6]{3-x}+\frac{\sin x}{\sqrt[4]{5 x-1}-\sqrt{5 x^{2}-16 x+3} .} \) 5. Упростите выражение \( \frac{\sqrt{a b} \cdot \sqrt[4]{b}}{(a-b) \cdot \sqrt[4]{\frac{a^{2}}{b}}-\frac{a^{2}+b^{2}}{a^{2}-b^{2}}} \). \( \begin{array}{l}\text { 6. Расположите в порядке убывания следующие числа: } \\ \sqrt{2}, \sqrt[3]{3}, \sqrt[5]{5} \text {. }\end{array} \) A wooden artifact from an ancient tomb contains 45 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) years A wooden artifact from an ancient tomb contains 45 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) \( \square \) years Example For each of the following equations, sketch its graph (a) \( y=\sqrt{x}-2 \) (b) \( y=\sqrt{x-2} \) (c) \( y=\sqrt{2-x} \) 4) Write a brief reflection on the sigificance of hyperbolic functions and their inverses i mathematics and real-world applic thions, such as in physics, engineering, and hyperboli genmery. Expresa como varios logaritmos: \( \ln \left(\sqrt[3]{x^{2} \sqrt{y}}\right) \) Seleccione una: a. \( \frac{1}{4} \ln x+\frac{1}{6} \ln y \) b. \( \frac{1}{3} \ln x+\frac{1}{3} \ln y \) c. \( \frac{2}{3} \ln x+\frac{1}{6} \ln y \) od. \( \frac{2}{5} \ln x+\frac{1}{3} \ln y \) Suppose that the functions \( u \) and \( w \) are defined as follows. \[ \begin{array}{l}u(x)=x+1 \\ w(x)=3 x+5 \\ \text { Find the following. } \\ (w \circ u)(-4)=\square\end{array} \] Find the domain and range of the function \( g(x)=\frac{1}{x^{2}+1} \). i) Sketch the graph of the function \( f(x)=-2+\sqrt{x+4} \). i) Find the value of \( k \) for which \( f(x)=x^{3}-k x^{2}+2 x \) is an odd functic i) Show that \( h(x)=\frac{1}{\sqrt{1-x}} \) is one to one and find its inverse.
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