Question

Which of the following is true about the function below 1/(sqrt x+10)A. It’s domain is (-10, ♾) and it’s range is (0, ♾)B. It’s domain is [-10, infinity ♾) and it’s range is (- ♾, 0) U ( 0, ♾) C. It’s domain is (-10, ♾) and it’s range is (-♾ , ♾) D. It’s domain is (-♾, 0] and it’s range is (0, ♾)

Answer 1

We are given the following function

f(x) = 1/√(x+10)

We want to find out the domain and range of this function.

Domain:

These are the values of x for which the function f(x) is defined.

Range:

These are the values of f(x) that we get after pluging the x values.

Now let us find out the domain of this function.

Try pluging x = -10 into the funtion and see what happens!

f(-10) = 1/√(-10+10) = 1/√(0) = 1/0 = undefined

Did you see? our function is undefined for x = -10 so that means the domain of the function is

Domain = x > -10

Another way to write this domain is

Domain = (-10, infinity)

Now let's come to the range

When we plug the x > -10 we get the corresponding values of function f(x)

Range = f(x) > 0

Another way to write this range is

Range = (0, infinity)