Question

Let f(x) = √6 − x. Find the domain of f(x). I really would love if someone could explain this to me too

Answer 1

\[f(x)=\sqrt{6-x}\]

Answer 2

Is that the problem?

Answer 3

yes

Answer 4

Do you understand that any number that makes the radicand negative cannot be in the domain?

Answer 5

yes

Answer 6

The radicand is 6-x. x can be all real numbers EXCEPT those that result in a negative value. So we start out by saying the domain is all real numbers and then we find the illegal values and exclude them.

Answer 7

Does it make sense so far?

Answer 8

yes

Answer 9

So let's say 6-x is negative and find those illegal values.

Answer 10

\[6-x<0\]

Answer 11

\[6<x\]

Answer 12

x>6

Answer 13

Those are the illegal numbers. So we say the domain is all real numbers except the ones that are greater than 6

Answer 14

There are different ways to state this. We could say that if x cannot be greater than 6 then it could be less than or equal to 6. So the domain is
\[x \le6\]

Answer 15

Some people prefer interval notation
\[(-\infty,6]\]

Answer 16

Others prefer setbuilder notation
\[{}{x|x \le6}\]

Answer 17

That would have braces around it.