Question

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

Answer 1

@Nnesha plssss

Answer 2

@agent0smith

Answer 3

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

Answer 4

yes

Answer 5

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

Answer 6

yeah, and then you simplify?

Answer 7

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

Answer 8

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

Answer 9

hmm

Answer 10

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

Answer 11

yeah do both work?

Answer 12

i got it right, it was whtai wrote :)

Answer 13

i have one more coudl you help wiht that?

Answer 14

hmm okay i'll try

Answer 15

ok thanks

Answer 16

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

Answer 17

f(x) = x+4 / 6

g(x) = 6x - 4

Answer 18

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 ??

Answer 19

yes

Answer 20

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

Answer 21

umm

Answer 22

yes?

Answer 23

i don't know it yet

Answer 24

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

Answer 25

ok

Answer 26

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

Answer 27

6(x+4)/6 -4

Answer 28

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

Answer 29

yers

Answer 30

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

Answer 31

thanks so muhc!

Answer 32

np :=)