How do you find the domain and range of #f(x)=sqrt(x-4)#?

1 Answer
Aug 6, 2017

Answer:

Here's what I got.

Explanation:

You know that when working with real numbers, you can only take the square root of a positive number.

This implies that the domain of the function, which includes all the values that #x# can take for which #f(x)# is defined, will have to account for the fact that

#x - 4 >= 0#

This is equivalent to saying that

#x >= 4#

You can thus say that the domain of this function is all real numbers that satisfy the above condition. In interval notation, this will be #x in [4, +oo)#.

The range of the function tells you the values that the function can take for values that #x# can take.

In this case, if you take the square root of a positive number, you will end up with a positive number, so

#f(x) = sqrt(x - 4) >= 0 color(white)(.)(AA) x in [4, +oo)#

The minimum value that #f(x)# can take occurs when #x = 4#, so

#f(4) = sqrt(4 - 4) = sqrt(0) = 0#

For any other value of #x >4#, you will have #f(x) >0#. In interval notation, the range of the function is #[0, + oo)#.

graph{sqrt(x-4) [-10, 10, -5, 5]}