Question

Y=lg(7-5x) найти область определения функции?

Answer 1

Решение задания смотри на фотографии

Answer 2

To find the domain of the function Y = lg(7-5x), we need to consider the restrictions on the input values (x) that allow the function to be well-defined. In mathematics, the logarithm function (lg or log) is only defined for positive arguments. Therefore, we must ensure that the expression inside the logarithm (7-5x) is greater than zero:

1. Set the argument greater than zero: 7 - 5x > 0

2. Solve for x: 5x < 7 x < 7/5

So, the domain of the function Y = lg(7-5x) is all real numbers x such that x < 7/5. In interval notation, the domain is (-∞, 7/5).