anonymous one year ago WILL BECOME FAN AND AWARD MEDAL!!! Make up any two functions f(x) and g(x), defined in terms of the variable x. For example, you might define f(x) = x – 15 and g(x) = 3x2. (Use different examples.) Then provide the compositions of the two functions f(g(x)) and g(f(x)). Which composite function has the greatest value for x = 10? Remember no right answer exists. Your answer completely depends on the functions you select.

1. anonymous

did you pick two functions?

2. anonymous

go ahead and make two up they can be anything, but you don't want to make them too hard, so stick with something simple

3. anonymous

once you have them we can do this easy

4. anonymous

f(x)= x+7 and g(x)= 1/x+7 were the functions I thought to use for this.

5. anonymous

$f(x)=x+7,g(x)=\frac{1}{x+7}$ like that?

6. anonymous

or was $$g(x)=\frac{1}{x}+7$$ either way we can do it

7. anonymous

you pick

8. anonymous

the second one was how I meant to put the second function. sorry ^.^"

9. anonymous

ok brave to use a denominator but no problem lets compute $f(g(x))$ first

10. anonymous

always work from the inside out $f(g(x))=f(\frac{1}{x}+7)$ is a fist step

11. anonymous

then since $$f9\heartsuit)=\heartsuit +7$$ you have ' $f(\frac{1}{x}+7)=\frac{1}{x}+7+7$ or more simply $\frac{1}{x}+14$

12. anonymous

$f(x)=x+7$ and $g(x)= \frac{ 1}{ x } +7$ this is how they should look

13. anonymous

yeah got it

14. anonymous

that makes $f(g(x))=f(\frac{1}{x}+7)=\frac{1}{x}+7+7=\frac{1}{x}+14$

15. anonymous

Sorry. My computer is messing up so I'm having a hard time seeing your responses. I'm not sure why open study isn't working properly for me, but it isn't...

16. anonymous

yeah for me too

17. anonymous

did you see the last one?

18. anonymous

Yes! And thank you for your help! I really do appreciate it :3

19. anonymous

for the next one it is a bit tricker

20. anonymous

$g(f(x))=g(x+7)=\frac{1}{x+7}+7$

21. anonymous

you can replace $$x$$ by 10 in both of those for $g(f(10))$ you will get $\frac{1}{10+7}=7=\frac{1}{17}+7=7\tfrac{1}{17}$

22. anonymous

you mean to get the result for Which composite function has the greatest value for x=10?

23. anonymous

right

24. anonymous

Sorry >.< late response again. But I believe I understand the material. ^w^

25. anonymous

ok good stay cool

26. anonymous

You too! ^w^ Thanks for the help @satellite73 :3