anonymous
  • anonymous
For f(x)=1/x-5 and g(x)=x^2+2 Find the expression for g(x). Substitute the value of g(x) into the function f(x) in place of x to find the value of f(g(x))
Mathematics
chestercat
  • chestercat
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Astrophysics
  • Astrophysics
So we're looking for f(g(x))?
anonymous
  • anonymous
Looking for g(x) too! But not sure if it's just g(x)=x^2+2 orrr
Astrophysics
  • Astrophysics
That just means plug in function g(x) where ever there is an x in f(x)

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Astrophysics
  • Astrophysics
g(x) is just x^2+2
Astrophysics
  • Astrophysics
If your f(x) = 1/(x-5) or is it (1/x)-5
anonymous
  • anonymous
it's 1/(x-5)
Astrophysics
  • Astrophysics
Ok, always put brackets! :) So go ahead and find f(g(x)) as I told you how to
anonymous
  • anonymous
I got 1/(x^2-3)
Astrophysics
  • Astrophysics
\[f(g(x)) = \frac{ 1 }{ (x^2+2)-5 }\]
anonymous
  • anonymous
It also has a part 2 that says: (gof)(6) a. find f(6) and b Substitute the value you found in Part 1 into g(x) to find g(f(6))
Astrophysics
  • Astrophysics
So yes, you're right :)
anonymous
  • anonymous
thanks!
Astrophysics
  • Astrophysics
(g o f)(x) is the same thing as g(f(x))
anonymous
  • anonymous
oh, so do i just plug in 6 to 1/(x^2-3) ?
Astrophysics
  • Astrophysics
So plug in function f(x) in g(x) then plug in 6 for (g o f)(6)
Astrophysics
  • Astrophysics
No, that's f(g(x))
anonymous
  • anonymous
oh so is it 1/(x-5) + 2
Astrophysics
  • Astrophysics
\[g(f(x)) = \left( \frac{ 1 }{ x-5 } \right)^2+2\]
anonymous
  • anonymous
Do i need to simplify that? or no
Astrophysics
  • Astrophysics
Just find g(f(6))
anonymous
  • anonymous
wait, is Find F(6) just plugging in 6 to f(x)
anonymous
  • anonymous
and g(f(6)) is the equation you gave? for part b
Astrophysics
  • Astrophysics
\[g(f(x)) = \left( \frac{ 1 }{ x-5 } \right)^2+2\] \[g(f(6)) = \left( \frac{ 1 }{ 6-5 } \right)^2+2\]
anonymous
  • anonymous
So it's 3 for the question that asks: Substitute the value you found in Part 1 into g(x) to find g(f(6))
anonymous
  • anonymous
and there's another question that says find f(6) so would that just be 1
Astrophysics
  • Astrophysics
Can you post the question, it's a bit confusing with all the notation
Astrophysics
  • Astrophysics
Especially when you're not using LaTeX
anonymous
  • anonymous
1) Find f(6). 2) Substitute the value you found in Part 1 into g(x) to find g(f(6))
Astrophysics
  • Astrophysics
I mean take an image of the question
Astrophysics
  • Astrophysics
and post it here
anonymous
  • anonymous
oh sorry! hold on
Astrophysics
  • Astrophysics
Yeah, I'm not sure which question is connected to what, so it's a bit confusing :P
anonymous
  • anonymous
anonymous
  • anonymous
it was separated into two pages, sorry!
Astrophysics
  • Astrophysics
Well I'm not sure why you didn't just take a picture of the full page, but it seems incomplete, your question for part A seems as if it wants you to find a expression using g(x) from the graph.
anonymous
  • anonymous
Oh, sorry ignore the graph, it's a different question. sorry!!
Astrophysics
  • Astrophysics
Huh? Then this really makes no sense, are the pages both completely different questions?
anonymous
  • anonymous
Nope, they're supposed to go together
Astrophysics
  • Astrophysics
Oh I see, the graph is on a different piece of paper!
anonymous
  • anonymous
yeah!! sorry haha :/
Astrophysics
  • Astrophysics
Ok, so lets do it all over again
Astrophysics
  • Astrophysics
We're given \[f(x) = \frac{ 1 }{ x-5 } ~~~\text{and}~~~~g(x) = x^2+2 \] Part 1, A seems they just want you to find the expression for g(x) meaning they are just seeing if you understand the question, so it's just \[g(x) = x^2+2\] part B wants you to find the f(g(x)) so we take function g(x) and plug it into f(x) \[f(g(x)) = \frac{ 1 }{ (x^2+2)-5 }\]
Astrophysics
  • Astrophysics
You can do the simplifications, now lets move on to part 2
Astrophysics
  • Astrophysics
We need to find f(6) that just means we need to find \[f(6) = \frac{ 1 }{ 6-5 }\] which gives us what?
anonymous
  • anonymous
1!
Astrophysics
  • Astrophysics
Good
anonymous
  • anonymous
and so B would be 3 right?
Astrophysics
  • Astrophysics
Lets see
Astrophysics
  • Astrophysics
It's asking us to substitute the value we found in part 1, into g(x) so we can find g(f(6))
anonymous
  • anonymous
yup! so I would just find g(f(x)) right?
Astrophysics
  • Astrophysics
What we found in part 1 was \[g(x) = x^2+2\]
Astrophysics
  • Astrophysics
Is the one they are referring to I believe
Astrophysics
  • Astrophysics
So all you need to do here is, find g(f(x)) first then g(f(6))
Astrophysics
  • Astrophysics
\[g(f(x)) = \left( \frac{ 1 }{ x-5 } \right)^2+2\]
anonymous
  • anonymous
I got 3
Astrophysics
  • Astrophysics
\[g(f(6)) = \left( \frac{ 1 }{ 6-5 } \right)^2+2\]
anonymous
  • anonymous
so yes, 3?
Astrophysics
  • Astrophysics
Yeah
anonymous
  • anonymous
Thanks so much for your help!! :))
Astrophysics
  • Astrophysics
So what this question is trying to get across is, you knowing what the notation means and what exactly these compositional functions are doing. So notice we actually took what we solved f(6) and just plugged in g(x)
anonymous
  • anonymous
I get it now haha :) thanks!!
Astrophysics
  • Astrophysics
We could've very well put \[g(f(6)) = f(6)^2 + 2 = 1^2+2\]
Astrophysics
  • Astrophysics
Np

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