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.

Question

anonymous · Answer

did you pick two functions?

anonymous · Answer

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

anonymous · Answer

once you have them we can do this easy

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

you pick

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

yeah got it

anonymous · Answer

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

anonymous · Answer

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...

anonymous · Answer

yeah for me too

anonymous · Answer

did you see the last one?

anonymous · Answer

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

anonymous · Answer

for the next one it is a bit tricker

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

right

anonymous · Answer

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

anonymous · Answer

ok good 
stay cool

anonymous · Answer

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