Find the domain in #y=sqrt(4-x)#?

1 Answer
Mar 19, 2018

#x<=4# or #(-oo,4]#

Explanation:

Since this is a square root, the values inside cannot be lesser that 0. Else, you would end up with an imaginary number. So, with that information, we can write the inequality:

#4-x>=0#

Solve for #x#:

#=> -x>=0-4#

#=>-x>=-4#

Now, when we multiply both sides by a negative, we have to switch the signs:

#(-1)-x<=(-1)-4#

#x<=4#

We can also represent this as:

#(-oo,4]#

And there we have our answer.