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Home Question Bank Math Algebra Archive 2024 November 01

Algebra Questions from Nov 01,2024

Browse the Algebra 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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Find the inverse for each of the following functions. \( s(x)=\frac{3}{x+2} \) \( s^{-1}(x)=\square \) \( g(x)=\sqrt[3]{3 x-9} \) \( g^{-1}(x)=\square \) \( k(x)=6 x-4 \) \( k^{-1}(x)=\square \) \( r(x)=13 x^{3}+4 \) \( r^{-1}(x)=\square \) Let \( f(x)=\frac{x+2}{x+7} \) \( f^{-1}(-7)=\square \) Find the inverse of \( f(x)=\frac{x-3}{-2 x-5} \) \( f^{-1}(x)=\square \) Math 110 Course Resources - Exponential \& Logarithmic Functions Course Packet on solving for an unknown exponent Consider the equation \( 2^{t^{2}-24}=(1 / 4)^{t} \). Enter the number of solutions of the above equation. Determine the values of \( t \) that solve the above equation. Enter your answer as a comma-separated list of values. The order of the values does not matter. Enter DNE if there are no solutions. - Exponential \& Logarithmic Functions Course Packet on solving for an unknown exponent Consider the equation \( 2^{2 x}-3 \cdot 2^{x}+2=0 \). Enter the number of solutions of the given equation. Determine the values of \( x \) that solve the given equation. Enter your answer as a comma-separated list of values. The order of the values does not matter. Enter DNE if there are no solutions. (a) Find the inverse function of \( f(x)=4 x-8 \). \( f^{-1}(x)= \) (b) The graphs of \( f \) and \( f^{-1} \) are symmetric with respect to the line defined by \( y= \) IVIDAD 3 Valor ( \( \mathbf{3 0} \) puntos) Resuelve las siguientes ecuaciones: \( y \) hacer la comprobaci \( \begin{array}{ll}5^{1-3 x}=\frac{1}{5} & \text { d) } 3^{2 x+5}=3^{x-1} \\ 2^{2 x-1}=4 & \text { e) } 7^{t+3}=\frac{1}{7} \\ \left(e^{4}\right)^{x} e^{x^{2}}=e^{12} & \text { f) } e^{x} e^{3 x}=e^{x-1}\end{array} \) \( ( 3 ^ { 4 } ) \boxed { \square } = 3 ^ { 28 } \) \( \left\{ \begin{array} { c } { x y + y ^ { 2 } = 4 } \\ { x ^ { 2 } - 3 x y + 1 = - y ^ { 2 } } \\ { 3 x ^ { 2 } + 3 y ^ { 2 } = 13 + x y } \end{array} \right. \) The common factor of \( x^{2}+6 x-7 \) and \( x^{2}-49 \) is
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