Question

Find the domain of the radical function.

Answer 1

PLEASE HELP if you can show steps please

Answer 2

you dont know anything
just asking help

Answer 3

the domain of the function will be in other words
"what values can 'x' take and YET not make the square root NEGATIVE?"

so, what value for "x" will yield a negative number inside the root you think?

Answer 4

x < with a line under 7?

Answer 5

let's try say 5 x = 5
\(\color{blue}{\sqrt{7-(5} \implies \sqrt{2}}\)
so, that didn't make it negative, thus "x" can take that value, so 5 is part of the domain

Answer 6

so, what will make the inside of the root, negative?

Answer 7

did i get the correct answer?

Answer 8

what makes you think is \(x \le 7 \large \ ?\)

Answer 9

i looked it up on how to solve it n i got that

Answer 10

yes, why is it right though? how do you even know is right?

Answer 11

im guessing you would plug it back in?

Answer 12

when they ask for the domain on an expression with a root, usually is meant, what would NOT make the root negative

Answer 13

so inside the root you have 7-x
so, what values for "x" will KEEP the expression POSITIVE?
is pretty much what's being asked

Answer 14

so, let's try a few "x"
say try
x = 2, 3, 4, 7, 9, 11
try those

Answer 15

you want me to plug those numbers in?

Answer 16

yeah

Answer 17

11 and 9 wouldnt work

Answer 18

to see which of those numbers for "x", will make keep the expression POSITIVE

Answer 19

11 and 9 wouldn't? why not?

Answer 20

cuz they give you a negative number

Answer 21

ohhh
how about 7?

Answer 22

gives you 0

Answer 23

how would you do that then

Answer 24

so, if x is 2, 3, 4 ,5, 6 you get some POSITIVE value
if x is 7, you get 0
after 7, the expression goes into negative

so the values "x" can take while keeping the expression POSITIVE
are the values of 7 OR LESS
so "x can be equals to 7 or less than 7" that is \(\huge\color{blue}{ x \le 7}\)

Answer 25

thanx that really helps

Answer 26

that one is done the same exact way
plug values for "x", if it becomes 0 or more is fine
once it "below" 0, or negative, then that's where the domain stops

Answer 27

its multiple choice

Answer 28

if you notice 2*3 = 6, so
6-2(3) = 6-6 =0
so x can be 3 or LESS