## anonymous one year ago Find f(x) and g(x) so that the function can be described as y = f(g(x)). y = two divided by x squared + 9

1. anonymous

@Nnesha plssss

2. anonymous

@agent0smith

3. Nnesha

$y=\frac{ 2 }{ x^2 }+9$ like this ?

4. anonymous

yes

5. Nnesha

f(g(x)) meaning substitute x for g(x) function

6. anonymous

yeah, and then you simplify?

7. Nnesha

right but this one is backwardz u have to find f(x) and g(x) from$y=\frac{ 2 }{ x^2 }+9$

8. anonymous

is f(x) = 2/x + 9 and g(x) = x^2

9. Nnesha

hmm

10. Nnesha

could be this $\frac{ 2 }{ x^2 } +9$ g(x) =x hmmm

11. anonymous

yeah do both work?

12. anonymous

i got it right, it was whtai wrote :)

13. anonymous

i have one more coudl you help wiht that?

14. Nnesha

hmm okay i'll try

15. anonymous

ok thanks

16. anonymous

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = Quantity x plus four divided by six and g(x) = 6x - 4

17. anonymous

f(x) = x+4 / 6 g(x) = 6x - 4

18. Nnesha

alright first try f(g(x))=x substitute x for g(x) function $\huge\rm f(\color{ReD}{g(x}))=\frac{( \color{ReD}{6x-4} )+ 4}{ 6 }$ now solve right side is it equal to x ??

19. anonymous

yes

20. Nnesha

alright now 2nd one g(f(x) ) is this equal to x ?

21. anonymous

umm

22. anonymous

yes?

23. Nnesha

i don't know it yet

24. Nnesha

substitute x for f(x) function into f(x)

25. anonymous

ok

26. Nnesha

$\huge\rm g(\color{ReD}{f(x)})=6\color{ReD}{x}-4$ replace x with (x+4)/6

27. anonymous

6(x+4)/6 -4

28. Nnesha

right $6(\frac{x+4 }{ 6 })-4$ is it equal to x ?

29. anonymous

yers

30. Nnesha

both are equal that shows both are inverse of each other f(g(x)) = g(f(x))

31. anonymous

thanks so muhc!

32. Nnesha

np :=)

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