Question

FoG Question! Algebra 2.
Question is in picture Thanks!
http://imgur.com/vW0jyYN

Answer 1

Can someone help me solve this?

Answer 2

\[f(x)=\frac{1}{x-5}\]
\[g(x)=\sqrt{x+2}\]

Answer 3

fog(x) = f(g(x))

Answer 4

the domain of \(g(x)\) is \(x\geq -2\) as a start

Answer 5

then
\[f(g(x))=f(\sqrt{x+2})=\frac{1}{\sqrt{x+2}-5}\]

Answer 6

domain has the same restriction as before, namely \(x\geq -2\) but you also have to make sure that the denominator is not zero

Answer 7

so set
\[\sqrt{x+2}-5=0\] and solve for \(x\)

Answer 8

so the domain is \[[-2,\infty) \]

Answer 9

no careful here

Answer 10

that confuses me the most

Answer 11

you cannot have a zero in the denominator, so you still have to solve
\[\sqrt{x+2}-5=0\]

Answer 12

@GrizzlySharkk
can you now tell for what value/s of x is denominator zero?

Answer 13

which you can just about do in your head
if \[\sqrt{x+2}-5=0\iff \sqrt{x+2}=5\iff x+2=25\iff x=23\]

Answer 14

so you have two restrictions,
\[x\geq -2,x\neq 23\]

Answer 15

-2 make x a zero @harsimran_hs4 and square roots cant be negative

Answer 16

at the risk of repeating myself, you have to make sure that the denominator is not zero
the denominator is
\[\sqrt{x+2}-5\]

Answer 17

and so \(x\) cannot be 23
if \(x=23\) you get
\[\sqrt{23+2}-5=\sqrt{25}-5=5-5=0\] which is forbidden in the denominator

Answer 18

-2 is perfectly fine
sqrt should not be negative
zero is allowed

Answer 19

@satellite73 ohh ok thank you so much

Answer 20

@GrizzlySharkk
satellite73 has shown the steps to find when denominator is zero

Answer 21

@harsimran_hs4 thank you so much, how do i write the domain out?

Answer 22

domain :
x >= -2 and x (not equal to) 23
[use the symbol for not equal to]

or

\[x \in [-2 , \infty) - {{23}} \]

Answer 23

put that 23 in {23} form
to show a set containing 23 should be removed

Answer 24

@GrizzlySharkk clear ??

Answer 25

@harsimran_hs4 I am doint the problem on a paper, now i am going to send you the picture through here. Please tell me if i got it right

Answer 26

ok

Answer 27

@harsimran_hs4 @satellite73 http://imgur.com/yc0kMmA is this right?

Answer 28

the smiley face is there so i don't get confused with the value of X

Answer 29

yes it is right!!

Answer 30

@harsimran_hs4 THANK YOU!!!

Answer 31

:)