# How do you find the domain and range algebraically of #f(x)=1/sqrt(x-4)#?

##### 1 Answer

Your function has a square root but also this square root is in the denominator of a fraction.

So, what you wan is to avoid values of

1) make the argument of the square root NEGATIVE (you cannot find a real number as solution of a negative square root);

2) make the denominator equal to ZERO (you cannot evaluate a division by zero).

To express the above points mathematically you write that

This means that you can accept only values that satisfy:

When you get near

So your domain will be all the positive

With a range for

Or graphically:

graph{1/sqrt(x-4) [-10, 10, -5, 5]}