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Home Question Bank Math Pre Calculus Archive 2025 January 24

Pre-calculus Questions from Jan 24,2025

Browse the Pre-calculus Q&A Archive for Jan 24,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Find functions \( f \) and \( g \) so that \( f \circ g=H \). \( H(x)=|2 x+9| \) Choose the correct pair of functions. A. \( f(x)=|-x|, g(x)=\frac{x-9}{2} \) B. \( f(x)=2 x+9, g(x)=|x| \) C. \( f(x)=\frac{x-9}{2}, g(x)=|-x| \) D. \( f(x)=|x|, g(x)=2 x+9 \) Sec 6.6 Inverse Trig: Probien 3 (1 point) Find the domain and the range of \( g(x)=\sin ^{-1}(3 x+1) \), Domain: \( \square \leq x \leq \square \) Range: \( \square \leq y \leq \square \) Note: You can earn partial credit on this problem. A psychologist is studying the capacity of the human mind to process information. He has found that the percentage of information one particular participant can recall after \( t \) months have passed can be modeled by the following logarithmic function. \[ f(t)=89-23 \ln (t+1) \text {, where } 1 \leq t \leq 12 \] What percentage of information is retained after 10 months? Round your answer to the nearest whole percentage, if necessary. Answer 2 Points Prev Keyboard Shortcuts Nexpt 19. Якого найменшого значення набуває функція \( y=(2 \cos 5 x-0,5) / 5 \) STABIUSU SE LE FUNZIONI SONO INIETIIVE, SURIETTIVE OBIETTIVE \( f(x)=-x^{2} \) An arithmetic and a geometric sequence are combined to form the pattern, which is given by: \( P_{n}=\frac{1}{7} ; \frac{1}{3} ; \frac{2}{2 x} ; \frac{1}{9} ; \frac{1}{3 x} ; \frac{1}{27} ; \ldots \) 2.2.1 Write down the next TWO terms of the pattern. 2.2.2 Determine the general term \( \left(I_{n}\right) \) for the odd terms of this pattern. Write down your answer in terms of \( x \). 2.2.3 Calculate the value of \( P_{26} \). 2.2.4 If \( \sum_{n=1}^{2 \pi} P_{n}=33,5 \), determine the value of \( x \). \( \left. \begin{array} { l } { y = a ( 1 - r ) ^ { t } } \\ { y = 100,000 ( 1 - 0.02 ) ^ { t } } \\ { y = 100,000 ( 0.98 ) ^ { t } - 4 } \end{array} \right. \) nich graph represents an exponential function? Para qué valores de \( x \) es discontinua la función \( f(x)=\frac{x^{2}+x-6}{x^{2}+4 \cdot x} \) ? ditar la solución de la forma siguiente: \( \left\{x=x_{1}, x=x_{2}, \ldots\right\} \) donde \( x_{1}, x_{2}, \ldots \) son los puntos de discontinuidad. Encuentra el polinomio de interpolación de Newton que pasa p los puntos \( (1,1),(2,4) \) y \( (3,9) \). Respuesta: El polinomio de interpolación es \( P(x)=x^{2} \)
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