Question

will give medal for anwser.

Answer 1

What is f(g(x))?

Answer 2

\[
f(g(x)) =\sqrt{8(x-3)}

\]

Answer 3

When is the square root defined? Can you take \(\sqrt {-5}\) as a real number?

Answer 4

Are you with me?

Answer 5

i just do not understand

Answer 6

To be able to take the square root of a number, this number must be positive or zero. Do you know that?

Answer 7

i did not.

Answer 8

Do now

Answer 9

For example
\[
\sqrt{25}=5
\]
but \[
\sqrt{-25}
\]
is not a real number and is therefore not defined as such

Answer 10

ok got it

Answer 11

What is under the square root in your composed function
\[
f(g(x))=\sqrt{ 8(x-3)}
\]
?

Answer 12

What is under the square root is
\[
8(x-3)
\]
this quantity must be \( \ge 0\)

Answer 13

What values of x will do that?

Answer 14

do i solve for x?

Answer 15

\[
(x-3)\ge 0\\
x\ge 3
\]

Answer 16

So the domain is
\[
[3, \infty[
\]

Answer 17

What is the smallest number in this interval?

Answer 18

wouldnt it be 3?

Answer 19

Yes

Answer 20

So what is the answer?

Answer 21

is it 3? how would i find out the smallest number

Answer 22

Yes it is 3.
If the numbers you are dealing with are 3 and all the numbers bigger than 3.
What would be the smaller one?

Answer 23

the 3

Answer 24

so the smallest number in the domain is 3 ?

Answer 25

was correct thanks

Answer 26

yes