Question

Найти обратную функцию y=4x/2x-1?

Answer 1

У=4х/(2х-1)
у(2х-1)=4х
2ху-у=4х
4х-2ху=-у
х(4-2у)=-у
х=-у/(4-2у)
выразили Х теперь меняем местами Х  и У
у=-х/(4-2х)

Answer 2

У(2х -1) = 4х
2ху -у = 4х
2ху -4х = у
х(2у -4) = у
х = у/(2y - 4)
Ответ: у = х/(2х -4)

Answer 3

Finding the Inverse Function of y = (4x)/(2x-1)

To find the inverse function of y = (4x)/(2x-1), we need to solve for x in terms of y. Let's go through the steps:

Step 1: Start with the given equation: y = (4x)/(2x-1).

Step 2: Multiply both sides of the equation by (2x-1) to eliminate the denominator: y(2x-1) = 4x.

Step 3: Distribute y to both terms on the left side: 2xy - y = 4x.

Step 4: Move all terms involving x to one side of the equation: 2xy - 4x = y.

Step 5: Factor out x on the left side: x(2y - 4) = y.

Step 6: Divide both sides of the equation by (2y - 4) to solve for x: x = y/(2y - 4).

Therefore, the inverse function of y = (4x)/(2x-1) is x = y/(2y - 4).