Question

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

Answer 1

\[f(x)=\sqrt{2-x}\]

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

but its positive ??

Answer 7

I'm not sure what you mean

Answer 8

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

Answer 9

yes exactly, so whatever number that is in the square root is either

a) zero

or

b) positive

Answer 10

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

Answer 11

is the answer x ≤ 2

Answer 12

correct! good work !!

Answer 13

i missed you @ganeshie8