## anonymous 5 years ago find the domain of the composite function f o g f(x) = x+4; g(x)= 9/x+6

1. anonymous

i think it is x not equal to -6

2. amistre64

the domain of the function f(g(x)) doesnt change any from it component parts. f(x) can use anything ; but g(x) cant use -6 so the domain of the composite is everything but "-6"

3. anonymous

4. amistre64

g(f(x)) would give us an additional ixnay for x... in that we might not be able to use -10

5. anonymous

yes ..in the case of g o f

6. anonymous

it is x not equal to 10

7. amistre64

if we were to consider functions that would perhaps"cancel"out an inapproriate domain, then the original domains would still take precident

8. amistre64

your gonna tell me im wrong..aintcha :)

9. anonymous

so ?? what say tamas?

10. anonymous

If $f(x)=x+4\textrm{ and }g(x)=\frac{9}{x+6}$ then $(f\circ g)(x)=f(g(x))=\frac{9}{x+6}+4.$ So $D_{f\circ g}=\mathbb{R}\backslash\{-6\}.$

11. anonymous

I concur with gorbe.tamas.