Question

Найдите множество значений функции y=1/x-1

Answer 1

Функция y=1/x - множество значений все числа кроме 0
функция y=1/x-1 - множество значений все числа кроме -1

Answer 2

Function Values for y = 1/x - 1

The function y = 1/x - 1 represents a hyperbolic function. To find the values of this function, we can substitute different values of x and calculate the corresponding y values.

1. Calculation of Function Values: - When x = 1, y = 1/1 - 1 = 1 - 1 = 0. - When x = 2, y = 1/2 - 1 = 0.5 - 1 = -0.5. - When x = 3, y = 1/3 - 1 = 0.33 - 1 = -0.67.

2. Graphical Representation: - The graph of the function y = 1/x - 1 is a hyperbola, and it approaches the x and y axes as x approaches positive or negative infinity.

3. Domain and Range: - The domain of the function y = 1/x - 1 is all real numbers except x = 0, as division by zero is undefined. - The range of the function y = 1/x - 1 is all real numbers except y = -1, as the function approaches but never reaches y = -1.

4. Additional Information: - The function y = 1/x - 1 is a type of rational function, and its graph exhibits asymptotic behavior as x approaches 0 and as x approaches positive or negative infinity.

In summary, the function y = 1/x - 1 takes on different values for different x inputs, and its graph forms a hyperbola with specific domain and range characteristics.