y= 1/x −7
Find the domain of this function
If you meant what you wrote, then the domain is all reals except x=0
If you meant y=1/(x-7) then the domain is all reals except x=7.
In other words, all reals except where the denominator is zero.
the denominator cannot equal zero. X can be all numbers, real and complex, but not seven
To find the domain of the function y = 1/x - 7, we need to determine the x-values for which the function is defined.
The domain of a function is the set of all possible input values (x-values) that will produce a valid output (y-value).
In this case, we need to consider two conditions:
1. The denominator cannot be equal to zero because division by zero is undefined.
2. The expression inside the square root must be greater than or equal to zero since the square root of a negative number is undefined.
Let's tackle each condition separately:
1. The denominator must not be equal to zero:
Since the denominator is x, we find the values for which x = 0. In this case, x cannot be zero because division by zero is undefined.
So, we exclude x = 0 from the domain.
2. The expression inside the square root must be greater than or equal to zero:
In this function, there is no square root operation involved. So we don't need to worry about this condition.
In summary, the domain of the function y = 1/x - 7 is all real numbers except x = 0.