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Home Question Bank Math Algebra Archive 2024 December 24

Algebra Questions from Dec 24,2024

Browse the Algebra Q&A Archive for Dec 24,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Which of the following is the inverse function of \( f(x)=\sqrt[3]{(x-2)}+1 \) ? Write \( \frac{1}{2} \log \left(x^{4}\right)-3 \log (x) \) as a single logarithmic expression A. \( \log \left(x^{\frac{3}{2}}\right) \) B. \( -\log (x) \) C. \( \frac{\log \left(x^{\frac{4}{3}}\right)}{\text { D. } \frac{1}{4} \log \left(x^{3}\right)} \) \[ f(x)=x^{2}-1 \quad g(x)=-k x^{2}+1 \quad h(x)=k x^{2}+k \] di \( \mathbb{R}_{\leqslant 2}[x] \) e sia \( B \) il sottospazio da essi generato. (i) Per quali valori di \( k \) i polinomi \( f(x), g(x) \) e \( h(x) \) sono una base di \( B \) ? (ix Calcolare la dimensione di \( B \) al variare di \( k \in \mathbb{R} \). (idi) Per quali valori di \( k \) il polinomio \( a(x)=2-k x+k x^{2} \) appartiene a \( B \) ? \( \left\{ \begin{array} { l } { 1.1 ) = \frac { 101 } { 100 } + \frac { 100 } { 101 } \quad b = \frac { 101 } { 100 } - \frac { 100 } { 101 } } \\ { a ^ { 2 } - b ^ { 2 } + 1 = ? } \\ { 2 x + y + z = 0 \times y z = - 18 \quad x ^ { 3 } + y ^ { 3 } + z ^ { 3 } = ? } \end{array} \right. \) Write \( \frac{1}{2} \log \left(x^{4}\right)-3 \log (x) \) as a single logarithmic expression \( a=\frac{101}{100}+\frac{100}{101} \) va \( b=\frac{101}{100}-\frac{100}{101} \) sonlari \( \begin{array}{llll}a^{2}-b^{2}+1 \\ \text { A)fodaning qiymatini toping. } \\ \begin{array}{llll}\text { A) } 1 & \text { B) } 2 & \text { C) } 4 & \text { D) } 5\end{array}\end{array} \) 2- Desarrolla las expreciones \( \left(4 m^{3} n^{2}-6 m^{3}\right)\left(6 m^{3}+4 m^{3} n^{2}\right) \) Solve \( -\frac{1}{6}\left[3-15\left(\frac{1}{3}\right)^{2}\right] \) EsERCIZIO 9.12 Trovare una base di \[ W=\left\{b+a x+a x^{2} \in \mathbb{R}_{\leq 2}[x] \mid a, b \in \mathbb{R}\right\} \] SVOLGIMENTO Una base è costituita dai polinomi 1 e \( x+x^{2} \) 98. Разность квадратов корней уравнения \( x^{2}+2 x+q=0 \) равна 12 . Найдите \( q \).
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