🧮 algebra

1. Problem: Find the inverse function $f^{-1}(x)$ for $f(x)=\frac{2x+1}{x-1}$, $x>1$. 2. To find $f^{-1}(x)$, start by setting $y=f(x)$:

1. **Stating the problem:** We are given a function $د(س) = س^2$ and asked several questions about its symmetry axis, zeros, and limits.

1. Muammo: 25 ta ketma-ket natural sonning yig'indisi 1000 ga teng. Bu sonlarning eng kichigi nechaga teng? 2. Ketma-ket sonlar: $x, x+1, x+2, \dots, x+24$.

1. The problem asks to find the sum of the numbers in the sequence starting from 10, 11, 12, 13, 14, 15, 16, ... up to 10 terms. 2. This is an arithmetic progression where the firs

1. The problem is to show that $$\sinh 2x = 2 \sinh x \cosh x$$. 2. Recall the definitions of hyperbolic sine and cosine:

1. The problem is to show that the parametric equations $x = a \cos \theta$ and $y = b \sin \theta$ represent the ellipse given by the equation $$\frac{x^2}{a^2} + \frac{y^2}{b^2}

1. The substitution method is used to solve a system of equations by expressing one variable in terms of the other and substituting it into the second equation. 2. Suppose the syst

1. The problem is to analyze the equation of the form $3x^2 + 2y^2 = 11$. 2. This is an equation of an ellipse because it is a sum of squared terms equal to a constant.

1. The problem asks to express the perimeter $P$ of a square as a function of its area $A$. 2. Let the side length of the square be $s$.

1. The problem is to analyze the equation of the form $3x^2 + 2y^2 = 11$. 2. This is an equation of an ellipse because it is a sum of squared terms equal to a constant.

1. The problem states that the parabola is given by the parametric equations $x=at^2$ and $y=2at$. 2. We want to show that these parametric equations represent the parabola $y^2=4a

1. The problem states that the parabola is given by the parametric equations $x=at^2$ and $y=2at$. 2. We want to show that these parametric equations represent the parabola $y^2=4a

1. The problem is to find the values of $x$ and $y$. 2. Since no equations or additional information are provided, we cannot determine unique values for $x$ and $y$.

1. The problem involves understanding ratios, formulas, and their solutions. 2. A ratio is a comparison of two quantities expressed as $a:b$ or $\frac{a}{b}$.

1. The problem is to understand and solve ratio formulas. 2. A ratio compares two quantities and is often written as $a:b$ or $\frac{a}{b}$.

1. समस्या को समझते हैं: हमें -2 के गुणज (multiples) लेने हैं और फिर प्रत्येक के बाद एक विषम संख्या (odd number) का वर्ग (square) जोड़ना है। 2. -2 के गुणज: $-2, -4, -6, -8, \dots$

1. **State the problem:** Solve the system of equations by substitution method: $$x + y = 2$$

1. The problem is to find the missing number in the sequence: 13, 11, 20, 16, ?, 35. 2. Let's analyze the pattern by looking at the differences between consecutive terms:

1. The problem is to solve the equation $$\sqrt{}\left(\;\right)w^2 - w + 3\left(\;\right) = 2w$$. 2. Notice that the expression $$\sqrt{}\left(\;\right)$$ and $$3\left(\;\right)$$

1. The user asks about the absence of $x$ in an equation. 2. To clarify, an equation without $x$ means it is either a constant or involves other variables.

1. The problem is to simplify and solve the equation $$\sqrt{x} \cdot w^2 - w + 3 = 2w$$ for $w$ in terms of $x$. 2. Start by rewriting the equation: