state the domain of the following function in interval notation
f(x)= sqrt 2x-9/x-5
plug in numbers to explain reasoning
The domain of the function is all real numbers except for x = 5, because the denominator cannot be zero.
In interval notation, the domain would be (-∞, 5) U (5, ∞).
If we plug in x = 5 into the function, we get:
f(5) = sqrt(2(5) - 9) / (5 - 5)
f(5) = sqrt(10 - 9) / 0
f(5) = sqrt(1) / 0
f(5) = 1 / 0
Since division by zero is undefined, x = 5 is not included in the domain of the function.