Question

This is a writing portion
Find f(x) and g(x) so the function can be expressed as y = f(g(x)).
y = Eight divided by x squared. + 4

Answer 1

@jim_thompson5910 my last question, I promise

Answer 2

@DanJS

Answer 3

@zepdrix

Answer 4

\[y=\frac{8}{x^2+4}\]??

Answer 5

yes

Answer 6

you got lots of choices for this one
suppose you had to evaluate this at say \(5\)
what would you do first if you wanted to compute \[\frac{8}{5^2+4}\]

Answer 7

would this work?

f(x) and g(x) are 2(x + 2) and 4x² respectively so that the function can be expressed as y = f(g(x)).

Answer 8

not if it was the one i wrote above,no
you need one to be a fraction of some kind

Answer 9

f(x) and g(x) are 2(x + 2) and 4x² then \[f(g(x))=f(4x^2)=2(4x^2+2)\]

Answer 10

oh, sorry. I didn't see what you sent. I was typing this..

Answer 11

go ahead and compute this number, see how you do it

Answer 12

\[\frac{8}{5^2+4}\]

Answer 13

what does compute mean

Answer 14

calculate, find the number, whatever

Answer 15

I keep getting 4.32

Answer 16

seems unlikely since the denominator is larger than the numerator
not really interested in the decimal answer, just in the method for computing the number

Answer 17

what is step one in finding \[\frac{8}{5^2+4}\] as in "order of operations" what do you do first ?

Answer 18

the denominator would be 29 right?

Answer 19

yes, so final answer would be \[\frac{8}{29}\] how did you get the 29?

Answer 20

5 squared is 25 plus 4 equals 29

Answer 21

right , step one was square 5, step two add 4, step three put it under 8

Answer 22

so you could say for \[y=\frac{8}{x^2+4}\] since step one is square put \(f(x)=x^2\) and \[g(x)=\frac{8}{x+4}\]
but you could do something else

Answer 23

you could combine the first two steps square and add 4, and put \[f(x)=x^2+4,g(x)=\frac{8}{x}\]

Answer 24

either one would work as would others

Answer 25

thank you

Answer 26

yw, hope it is more or less clear

Answer 27

Another way is to write out
\[\Large f(x) = \frac{8}{x^2+4}\]
Then highlight the x^2 term in red
\[\Large f(x) = \frac{8}{{\color{red}{x^2}}+4}\]
We can replace that with some function g(x). So I'm defining g(x) = x^2
\[\Large f(x) = \frac{8}{{\color{red}{x^2}}+4}\]
\[\Large f(x) = \frac{8}{{\color{red}{g(x)}}+4}\]

Answer 28

If we had \[\Large f(x) = \frac{8}{x+4}\] and g(x) = x^2, then evaluating f(g(x)) would give...


\[\Large f(x) = \frac{8}{x+4}\]
\[\Large f({\color{red}{x}}) = \frac{8}{{\color{red}{x}}+4}\]
\[\Large f({\color{red}{g(x)}}) = \frac{8}{{\color{red}{g(x)}}+4}\]
\[\Large f({\color{red}{g(x)}}) = \frac{8}{{\color{red}{x^2}}+4}\]