The range is negative numbers. The interval for the range is . ***You might want to look at your functions again because I don't see a choice that matches. Step-by-step explanation: Given functions:
We are asked to find the range of . I'm also going to look at the domain just to see if this possibly might change my range . is the inner function. So we will consider the domain of that function first. You only have to worry about division by zero for the function . Since we are dividing by , we don't want to be zero. So far the domain is all real numbers except . Now let's move out. exists for all numbers, . So we didn't want to include from before. Now let's put it together:
So the domain is still all real numbers except at since we cannot divide by 0 and is 0 when . with . is positive for all numbers except . So is negative for all numbers since negative divided by positive is negative. So the range is only negative numbers. Let's also look at the inverse:
Multiply both sides by :
Divide both sides by :
Take the square root of both sides: . So can't be 0 and it also can't be positive because the inside of the square root will be negative (since negative divided by positive results in negative).
This tells us that sodium has 11 protons and because it is neutral it has 11 electrons. The mass number of an element tells us the number of protons AND neutrons in an atom (the two particles that have a measurable mass). Sodium has a mass number of 23amu.
