Question

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))

Answer 1

So we're looking for f(g(x))?

Answer 2

Looking for g(x) too! But not sure if it's just g(x)=x^2+2 orrr

Answer 3

That just means plug in function g(x) where ever there is an x in f(x)

Answer 4

g(x) is just x^2+2

Answer 5

If your f(x) = 1/(x-5) or is it (1/x)-5

Answer 6

it's 1/(x-5)

Answer 7

Ok, always put brackets! :)

So go ahead and find f(g(x)) as I told you how to

Answer 8

I got 1/(x^2-3)

Answer 9

\[f(g(x)) = \frac{ 1 }{ (x^2+2)-5 }\]

Answer 10

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))

Answer 11

So yes, you're right :)

Answer 12

thanks!

Answer 13

(g o f)(x) is the same thing as g(f(x))

Answer 14

oh, so do i just plug in 6 to 1/(x^2-3) ?

Answer 15

So plug in function f(x) in g(x) then plug in 6 for (g o f)(6)

Answer 16

No, that's f(g(x))

Answer 17

oh so is it 1/(x-5) + 2

Answer 18

\[g(f(x)) = \left( \frac{ 1 }{ x-5 } \right)^2+2\]

Answer 19

Do i need to simplify that? or no

Answer 20

Just find g(f(6))

Answer 21

wait, is Find F(6) just plugging in 6 to f(x)

Answer 22

and g(f(6)) is the equation you gave? for part b

Answer 23

\[g(f(x)) = \left( \frac{ 1 }{ x-5 } \right)^2+2\] \[g(f(6)) = \left( \frac{ 1 }{ 6-5 } \right)^2+2\]

Answer 24

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))

Answer 25

and there's another question that says find f(6) so would that just be 1

Answer 26

Can you post the question, it's a bit confusing with all the notation

Answer 27

Especially when you're not using LaTeX

Answer 28

1) Find f(6).

2) Substitute the value you found in Part 1 into g(x) to find g(f(6))

Answer 29

I mean take an image of the question

Answer 30

and post it here

Answer 31

oh sorry! hold on

Answer 32

Yeah, I'm not sure which question is connected to what, so it's a bit confusing :P

Answer 33

it was separated into two pages, sorry!

Answer 34

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.

Answer 35

Oh, sorry ignore the graph, it's a different question. sorry!!

Answer 36

Huh? Then this really makes no sense, are the pages both completely different questions?

Answer 37

Nope, they're supposed to go together

Answer 38

Oh I see, the graph is on a different piece of paper!

Answer 39

yeah!! sorry haha :/

Answer 40

Ok, so lets do it all over again

Answer 41

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) \[f(g(x)) = \frac{ 1 }{ (x^2+2)-5 }\]

Answer 42

You can do the simplifications, now lets move on to part 2

Answer 43

We need to find f(6) that just means we need to find \[f(6) = \frac{ 1 }{ 6-5 }\] which gives us what?

Answer 44

1!

Answer 45

Good

Answer 46

and so B would be 3 right?

Answer 47

Lets see

Answer 48

It's asking us to substitute the value we found in part 1, into g(x) so we can find g(f(6))

Answer 49

yup! so I would just find g(f(x)) right?

Answer 50

What we found in part 1 was \[g(x) = x^2+2\]

Answer 51

Is the one they are referring to I believe

Answer 52

So all you need to do here is, find g(f(x)) first then g(f(6))

Answer 53

\[g(f(x)) = \left( \frac{ 1 }{ x-5 } \right)^2+2\]

Answer 54

I got 3

Answer 55

\[g(f(6)) = \left( \frac{ 1 }{ 6-5 } \right)^2+2\]

Answer 56

so yes, 3?

Answer 57

Yeah

Answer 58

Thanks so much for your help!! :))

Answer 59

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)

Answer 60

I get it now haha :) thanks!!

Answer 61

We could've very well put \[g(f(6)) = f(6)^2 + 2 = 1^2+2\]

Answer 62

Np