find the domain and range

Question

Y = the square root of 10x-40.

The 10x-40 is inside the square root.

Find domain and range

Answer 1

Because you cannot take a square root of a negative number and get a real number answer, this limits the domain (and the range as a consequence).  Remember, the domain is the list of all possible inputs or x-values that the function can use.

By solving the inequality below, you can find the values of x that provide a positive number to appear inside the square root:

 

10x - 40 ≥ 0

 

10x ≥ 40

x ≥ 4

 

Therefore, the domain is: {x|x ≥ 4}

 

The square root function has two solutions: one positive and one negative.  Unless otherwise indicated, we usually default to the positive root.  Since all positive real numbers have a square root value, all your answers will be greater than or equal to 0. 

 

Therefore, the domain is: {y|y ≥ 0}