<span>f(x) = sqrt(x-5) Domain: all real numbers greater or equal to 5
f(x) = 7/(x-8) Domain: all real numbers except 8
f(x) = sqrt(x) Domain: all positive real numbers and 0
f(x) = 8x Domain: all real numbers
The domain of a function is the set of all numbers for which that function is valid. You have 4 functions and 4 possible domains to choose from. Let's work each one out.
f(x) = sqrt(x-5)
You're not allowed to take the square root of a negative number. So the domain for this function would be all values of x >= 5. That way you're taking the square root of 0 or higher. Let's see if any of your choices match that.
And you have the choice "all real number greater or equal to 5"
f(x) = 7/(x-8)
You're not allowed to divide by 0. And the denomerator becomes 0 if x equals 8. So the domain is all real numbers except 8 which happens to be one of the choices.
f(x) = sqrt(x)
This is much like the 1st choice. You can't take the square root of a negative number. So the domain is all non-negative numbers. Looking at the choices, there isn't a match, but there's the choice "all positive real numbers and 0" which means the same thing. So that's the answer.
f(x) = 8x
I don't see anything that would make it impossible to evaluate this expression. So its' domain is all real numbers. And you have that as a choice.</span>
