Question

Find the domain of the composite function . Please show all of your work.
f(x) = x/x+9; g(x)= 45/x+5 Find the domain of the composite function . Please show all of your work.
f(x) = x/x+9; g(x)= 45/x+5 @Mathematics

Answer 1

\[f(g(x)) = \frac{\frac{45}{x+5}}{\frac{45}{x+5} + 9}\]

LCD at the denominator to get:

\[f(g(x)) = \frac{\frac{45}{x+5}}{\frac{90 + 9x}{x+5}}\]

Which is...

\[\frac{45}{\cancel {x+5}}\frac{\cancel {x+5}}{90+9x} \rightarrow \frac{45}{9(10+x)} \rightarrow \frac{5}{10+x}\]

So..

\[10 + x \neq 0 \rightarrow x \neq -10\]

Answer 2

wow, im impressed. is this the answer?

Answer 3

The answer of the domain is:

\[x \in R \neq {(-10)}\]

Answer 4

Thank you so much!!!

Answer 5

How did you get this?!

Answer 6

IM trying to figure out what the second function says. I can't read the bottom numbers. Can you tell me what they are?

Answer 7

f(g(x)) = \[\huge \frac{\frac{45}{x+5}}{\frac{90 + 9x}{x+5}}\]

\[\frac{45}{\cancel {x+5}}\frac{\cancel {x+5}}{90+9x} \rightarrow \frac{45}{9(10+x)} \rightarrow \frac{5}{10+x}\]

Answer 8

great. lol- thank you again! It was in a small print and I couldnt really tell what it was. :)

Answer 9

And if you have..

f(x) = x+1 and g(x) = 3...

The f(g(x)) is just sticking the value of g(x) inside of the f(x) so...

f(x) = 3+1 => 4.
So it's just a constant function y = 4.
Bye :)

Answer 10

ok- i forgot to put in the original equation that is was asking for fog...will that change this any?

Answer 11

(f ∘ g)(x) = f(g(x))

So no problem ;)

Answer 12

oh gotcha...ok- so really I dont have to worry about anything changing? lol

Answer 13

nope, different notation, same stuff.

Answer 14

cool.

Answer 15

but firstly you need to suppose that x not can being equal -9 and -5 so because than those freactions are undefined

Answer 16

fractions

Answer 17

sorry