Math Problem Statement

На рисунке изображены графики функций f(x) = a√x и g(x) = kx, пересекающиеся в точках A и B. Найдите абсциссу точки B.

Solution

The question in the image asks to find the abscissa (x-coordinate) of the point B where two functions intersect. These functions are:

  • f(x)=axf(x) = a\sqrt{x} (a square root function),
  • g(x)=kxg(x) = kx (a linear function).

We need to find the x-coordinate of the point of intersection, labeled as point B.

To solve this:

  1. Find the intersection points: Set f(x)=g(x)f(x) = g(x), meaning: ax=kxa\sqrt{x} = kx
  2. Solve for x: Square both sides of the equation to remove the square root and then solve for xx.

From the graph, the approximate values for f(x)f(x) and g(x)g(x) intersect visually at two points. We can use the graph to estimate these coordinates and compare with our algebraic solution to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Graphical Analysis
Intersection of Functions

Formulas

f(x) = a√x
g(x) = kx
Set f(x) = g(x) to find intersection

Theorems

Basic properties of square root functions
Linear equations and intersections

Suitable Grade Level

Grades 9-11