Question

Y = 6/ x-1 Знайти обл. визначення ф-ції

Answer 1

y=$\frac{6}{x-1}$;

x-1≠0

x≠1

D(y): x ∈ (-∞; 1) ∪ (1; +∞)  

Answer 2

To find the domain of the function Y = 6/(x - 1), we need to determine the values of x for which the function is defined. The domain of a function represents all the possible valid inputs (x-values) for which the function produces a real output (Y).

In this case, the function Y = 6/(x - 1) is defined as long as the denominator (x - 1) is not equal to zero. Division by zero is undefined in mathematics. So, we need to find the values of x that make the denominator equal to zero and exclude those from the domain.

To find the values of x that make the denominator zero, set x - 1 equal to zero and solve for x:

x - 1 = 0

Adding 1 to both sides:

x = 1

So, x = 1 is the value that makes the denominator (x - 1) equal to zero.

Now, to find the domain, simply state the valid values of x:

Domain: All real numbers except x = 1.

In interval notation, the domain can be expressed as:

Domain: (-∞, 1) U (1, ∞)

This means that the function Y = 6/(x - 1) is defined for all real numbers except x = 1.