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

1 Answer
Stefan V.
Aug 6, 2017

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]}

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