🧮 algebra

1. **State the problem:** We have an increasing function $f$ on its domain. We want to know which of the following functions is not necessarily increasing on its domain. 2. **Analy

1. The problem asks for the value of the 4th root of -81, which means finding a number $x$ such that $$x^4 = -81.$$ 2. Recall that raising any real number to the 4th power results

1. The problem is to compute the value of the expression $$\frac{1}{12} + \frac{2}{6} - \frac{2}{8}$$. 2. First, find a common denominator for the fractions. The denominators are 1

1. The problem asks to solve or simplify an expression using BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction). Since no specific expression for "question 2.

1. The problem is to divide the polynomial $x^3 - 2$ by $x^2 + 1$ using long division. 2. Set up the long division: divide the first term of the dividend $x^3$ by the first term of

1. Given $f(x) = x^2 + 3x - 4$: 1. a) Find $f(0)$:

1. **State the problem:** Find two non-equivalent polynomial functions $f(x)$ and $g(x)$ such that they have the same values at $x=0$ and $x=-3$, i.e., $f(0)=g(0)$ and $f(-3)=g(-3)

1. Diketahui matriks $$A=\begin{pmatrix}4 & 2 \\ -3 & -1\end{pmatrix}$$ dan $$B=\begin{pmatrix}2 & -1 \\ 3 & 0\end{pmatrix}$$. 2. Hitung determinan $$|A|$$:

1. Diketahui matriks $$M=\begin{pmatrix} x+5 & 4 & 1 \\ x+3 & x-4 & 1 \\ -2 & -4 & -1 \end{pmatrix}$$ dan kita ingin mencari nilai-nilai $$x$$ sehingga matriks $$M$$ bersifat singu

1. Diketahui matriks-matriks sebagai berikut: $$P=\begin{pmatrix}2 & 1 \\ 1 & c\end{pmatrix},\quad Q=\begin{pmatrix}2 & b \\ 2 & a \\ 1\end{pmatrix},\quad R=\begin{pmatrix}-1 & 1 &

1. The binomial theorem describes the algebraic expansion of powers of a binomial expression, i.e., expressions of the form $(a+b)^n$, where $n$ is a non-negative integer. 2. The t

1. We are given the price ratio of two vehicles as $8:7$. Let the original prices be $8x$ and $7x$ respectively. 2. After three years, the price of the first vehicle increases by 8

1. **Problem Statement:** Solve the equation $$(x + 3)(x + 5)(x + 7)(x + 9) = 9.$$ 2. **Step 1: Introduce substitutions for simplification.** Notice the expression involves four co

1. The problem asks whether the statement "As $x$ goes to positive infinity, $f(x)$ goes to positive infinity" is true or false for the given graph. 2. From the graph description,

1. Let's clarify the given expressions about the complex number $z$: - $z$ alone is the complex number itself.

1. The problem states: Given the function $f : [1, \infty) \to [1, \infty)$ defined by $$f(x) = 2^{x^{x-1}},$$

1. The user requests to solve a problem using only formulas, without options. 2. Since no specific problem is provided, I'll explain the general approach to solving algebraic equat

1. **Stating the problem:** We are given the function $$f : [1, \infty) \to [1, \infty)$$ defined by $$f(x) = 2^{x^{x-1}}$$. We need to find the inverse function $$f^{-1}(x)$$.

1. The problem is to find the degree of a polynomial or expression. 2. The degree of a polynomial is the highest power of the variable in the expression with a nonzero coefficient.

1. We are asked to expand the expression $$(x+4)(x-5)(x+3)$$. 2. First, expand two of the factors, for example, $(x+4)(x-5)$:

1. Stating the problem: Simplify the expression $$\sqrt{10^{400} \div 10^{220} \times 10^{80}}$$. 2. Apply the division rule for exponents: $$10^{400} \div 10^{220} = 10^{400-220}