Question

Are f(x)=(2)/(3)x+6 and g(x)=(3)/(2)x-9 inverse of each other.

Answer 1

no they aren't

Answer 2

find f-1(x) and it wont equal g(x)

Answer 3

f(x)=2/3x+6

An inverse of a function involves an x,y-interchange; that is, flip the x and y around and solve for y again.

Thus,

f(x) = y = 2 / (3x+6)
x = 2/(3y+6)
x(3y+6) = 2
3xy + 6x = 2
3xy = 2-6x
y = (2-6x)/3x

Since this doesn't match g(x), they are NOT inverses of one another.

OR... do you mean f(x)= (2/3)x+6 = y
x = (2/3)y + 6
x-6 = (2/3)y
(x-6)(3/2) = y
(3/2)x - 9 = y

In this case, they ARE inverses of one another. I'm not sure what you really meant so I gave you to scenarios for f[x].

Answer 4

This is how the question reads...Determine whether f(x) and g(x) are inverses of each other.
f(x)=(2)/(3)x+6
g(x)=(3)/(2)x-9

Answer 5

appreciate it so much, was just clarifiying the question:) Is the answer yes?

Answer 6

Yes, :)

Answer 7

is there something you don't understand ? ;o

Answer 8

Yes, Alot lol but I'm learning as I go. It helps for me to figure HOW it come to that answer.