Find the domain of the function:
f(s)=sqrt s-1 over s-4
the numerator is sqrt(s-1)
you may not take the sqrt of a negative number so s must be >/= 1
the domain also must skip the point where the denominator is zero; that is when s = 4
domain: all real numbers except 4
To find the domain of the given function f(s) = sqrt((s-1)/(s-4)), we need to consider the restrictions on the values that the variable "s" can take.
The primary restriction for the domain of this function is that the denominator (s-4) cannot be zero since division by zero is undefined. Therefore, we need to find the values of "s" that make the denominator zero.
Setting the denominator equal to zero, we have:
s - 4 = 0
Solving this equation, we find that s = 4.
So, the function is undefined at s = 4. Therefore, the domain of f(s) is all real numbers except for s = 4. In interval notation, the domain is (-∞, 4) U (4, ∞).