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Home Question Bank Math Pre Calculus Archive 2024 November 01

Pre-calculus Questions from Nov 01,2024

Browse the Pre-calculus Q&A Archive for Nov 01,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Let \( f(x)=(x-1)^{2} \) Give the largest domain on which \( f \) is one-to-one and non-decreasing. Give the range of \( f \). Find the inverse of \( f \) restricted to the domain above. \( f^{-1}(x)=\square \) Give the domain of \( f^{-1} \). Give the range of \( f^{-1} \). Answer parts (a)-(e) for the function shown below. \( f(x)=x^{3}-2 x^{2}-x+2 \) a. Use the leading coefficient test to determine the graph's end behavior. Which statement describes the behavior at the ends of \( f(x)=x^{3}-2 x^{2}-x+2 \) ? A. The graph falls to the left and to the right. B. The graph falls to the left and rises to the right. C. The graph rises to the left and falls to the right. D. The graph rises to the left and to the right. b) So sánh A và B biết \( \mathrm{A}=\frac{2024}{2^{2024}}+\frac{2023}{2^{2023}} ; B=\frac{2023}{2^{2024}}+\frac{2024}{2^{2023}} \) Si el resultado de una división de función racional es \( 3 x-7 \), tabula y encuent los pares ordenados de la asíntota. Use the leading coefficient test to determine the end behavior of the graph of the given polynomial function. \[ f(x)=2 x^{7}+8 x^{2}+8 x+1 \] MCQ problems 1) The range of \( f(x)=\frac{3}{x^{2}-1} \quad \) is .......... \( \begin{array}{llll}\text { a) } R & \text { b) } R-\{1,-1\} & \text { c) }]-\infty,-3] \cup] 0, \infty[ & \text { d) }[-3, \infty[ \end{array} \) \( z = ( \frac { 1 + i \sqrt { 3 } } { \sqrt { 2 } - i \sqrt { 2 } } ) ^ { 15 } \) 1. \( y=9-x^{2} ;[a, b]=[-3,3] \) Suppose \( H(x)=3 \sqrt{x}+2 \). Find two functions \( f \) and \( g \) such that \( (f \circ g)(x)=H(x) \). Neither function can be the identity function. (There may be more than one correct answer.) \( f(x)=\square \) \( g(x)=\square \) Begcin by graphing the standand square root function \( f(x)=\sqrt{x} \). Then use transformation of this graph to graph function \( g(x)=\sqrt{x+4}-2 \)
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