## sara1234 2 years ago Determine the domain of the function. f(x) is equal to the square root of two minus x. x ≤ 2 All real numbers x > 2 All real numbers except 2

1. sara1234

$f(x)=\sqrt{2-x}$

2. jim_thompson5910

Hint: You cannot take the square root of a negative number (and get some real number)

3. jim_thompson5910

So the radicand (the stuff inside the square root) can't be negative

4. sara1234

can you please teach me how to do this step by step PLEASE

5. jim_thompson5910

Similar example: Find the domain of $\Large g(x) = \sqrt{x+3}$ You can't take the square root of a negative number, so the radicand must be either 0 or positive. So... $\Large x+3 \ge 0$ $\Large x+3-3 \ge 0-3$ $\Large x \ge -3$ is the domain

6. sara1234

but its positive ??

7. jim_thompson5910

I'm not sure what you mean

8. sara1234

you said you can't take the square root of a negative number

9. jim_thompson5910

yes exactly, so whatever number that is in the square root is either a) zero or b) positive

10. nickhouraney

if your finding the domain of a square root your rules are that the number cant be negative. if you were taking the domain of a fraction the rules would be you cant have a zero on the denominator

11. sara1234

is the answer x ≤ 2

12. ganeshie8

correct! good work !!

13. sara1234

i missed you @ganeshie8