🧮 algebra

1. **Problem Statement:** Define the following terms with examples: (a) Function, (b) Even function, (c) Odd function, (d) Domain, (e) Range. 2. **Definitions and Examples:**

1. **Problem:** Given the equations $$a = \frac{1 - x^2}{1 + x^2}$$

1. **Problem Statement:** Verify the quantities of wheat, corn, and rice using the matrix inverse method given the system of linear equations from the fertilizer, water, and labor

1. **State the problem:** Solve the inequality $$\frac{x-1}{x} - x \leq 1 - \frac{x}{x+1}$$. 2. **Rewrite the inequality:** Bring all terms to one side to compare with zero:

1. **State the problem:** Solve the inequality $$\frac{x - 1}{x} - x < 1 - \frac{x}{n + 1}$$ for $x$. 2. **Rewrite the inequality:**

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases}\frac{x^2 - x}{x^2 - 1} & \text{if } x \neq 1 \\ 1 & \text{if } x = 1\end{cases}$$

1. The problem is to simplify or solve the given expression or equation using an easier method. 2. To make math easier, look for patterns like factoring, combining like terms, or u

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle that to isolate $x$, we perform inverse operations to both sides of the equati

1. **State the problem:** Solve the equation $a x^2 - x y = 3 f \ln x$ for one of the variables or simplify it.

1. The user provided multiple algebraic expressions and equations but asked to "Traite moi" which means "Process me" or "Solve for me" in French. 2. According to the guest rule, I

1. **State the problem:** Find the smallest value of $p$ for which the quadratic equation $$x^2 - 2(p+1)x + p^2 = 0$$ has real and equal roots. Then find the roots of the quadratic

1. **Problem:** Solve the radical equation $\sqrt{2x} = 12$ and determine if the solution is valid. 2. **Formula and rules:** To solve equations involving square roots, isolate the

1. **Problem statement:** Solve the radical equation $\sqrt{2x} = 12$ and determine if the solution is acceptable. 2. **Formula and rules:** To solve equations involving square roo

1. **State the problem:** Simplify the expression $$7\sqrt{18x^2} + \sqrt{48x^4} + \sqrt{x^8}$$. 2. **Recall the square root properties:**

1. Асуудлыг тодорхойлж эхэлье: Та бүх бодолтыг дэлгэрэнгүйгээр хүссэн байна. 2. Бодолтын жишээ авч үзье: Жишээ нь, $2x + 3 = 7$ тэгшитгэлийг бодъё.

1. **State the problem:** Simplify the expression $8n + 12 + (-9) - (-6n)$. 2. **Recall the rules:** When subtracting a negative, it becomes addition: $-(-6n) = +6n$. Also, combine

1. **State the problem:** Simplify and solve for $a$ given the expression: $$a = \ln \left( \left(\sqrt{e+1} - 1\right)^{2025} \right) + \ln \left( \left(\sqrt{e+1} + 1\right)^{202

1. **State the problem:** Simplify the expression $8n + (-6n)$. 2. **Recall the rule:** When adding terms with the same variable, add their coefficients.

1. **State the problem:** We are given the inequality $y \le 2x - 3$ and need to understand its meaning and graph. 2. **Explain the inequality:** This inequality means that the val

1. Problem (g): Simplify $ (3 - 4i) + (6 + i) $. Step 1: Add the real parts: $3 + 6 = 9$.

1. **Problem Statement:** Determine whether the relation in graph (b) is discrete, continuous, discontinuous, or neither. Then state its domain and range.