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Home Question Bank Math Pre Calculus Archive 2025 January 22

Pre-calculus Questions from Jan 22,2025

Browse the Pre-calculus Q&A Archive for Jan 22,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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The equation \( y=\log (x+1) \) has a vertical asymptote at: \( x=\square \) For the function \( f(x)=6^{x} \) calculate the following function values: \( f(4)= \) \( f(5)= \) On considère la fonction \( f \) définie de \( \mathbb{R} \) vers \( \mathbb{R} \) par: \( f(x)=\frac{|x|-2}{x+2} \) Détermine les restrictions de \( f \) à \( \mathbb{R}^{+} \)et à \( \mathbb{R}^{-} \backslash\{-2\} \) Answer the following True or False: For every \( x>0, e^{\ln (6 x)}-\ln \left(e^{6 x}\right)=0 \) True False Given the geometric series: \( 8 x^{2}+4 x^{3}+2 x^{4}+\ldots \) 3.1 Determine the \( \mathrm{n}^{\text {th }} \) term of the series. 3.2 For what value(s) of \( x \) will the series converge? 3.3 Calculate the sum of the series to infinity if \( x=\frac{3}{2} \). Nubraižyk funkcijos grafika: \( \begin{array}{llll}\text { a) } f(x)=2 x-3 ; & \text { b) } f(x)=x^{2}+2 x-8 ; & \text { c) } f(x)=(x-2)^{2}-4 ; & \text { d) } f(x)=\frac{6}{x} ; \\ \text { e) } g(x)=3 x ; & \text { f) } g(x)=(x-1)(x+1) ; & \text { g) } g(x)=\frac{1}{2} x^{2}+1 ; & \text { h) } g(x)=-\frac{1}{2} x^{2}+2\end{array} \) QUESTION 7 Suppose the functions \( f, g, h \) and \( l \) are defined as follows: \[ \begin{array}{l} f(x)=4 x^{2}-5 x+1 \\ g(x)=2 \sqrt{2-\frac{x}{2}}-x \\ h(x)=-\frac{1}{2} x+3 \\ l(x)=\log _{4}(x+3)-\log _{4}(x-2) \end{array} \] (a) Write down \( D_{f} \) and solve the inequality \( f(x) \leq 0 \). (b) Solve the equation \( g(x)=-4 \). (c) Solve the equation \( 4^{h(x)}=8 \). (d) Write down \( D_{l} \) and solve \( l(x)=\frac{1}{2} \). The height of the baseball thrown upward into the air \( t \) seconds after it is released is approximated by the function \[ h=-16 t^{2}+96 t+6 \] a. Find the maximum height of the baseball. \( \frac{a+i b}{a-i b} \) का कोणांक ज्ञात कीजिए। \( f(x)=\log _{2}(x+3) \) and \( g(x)=\log _{2}(3 x+1) \). (a) Solve \( f(x)=4 \). What point is on the graph of \( f \) ? (b) Solve \( g(x)=4 \). What point is on the graph of \( g \) ? (c) Solve \( f(x)=g(x) \). Do the graphs of \( f \) and \( g \) intersect? If so, where? (d) Solve \( (f+g)(x)=7 \). (e) Solve \( (f-g)(x)=6 \).
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