Question

help? find the inverse of the given function and use composition to justify the results of: g(x)= x-3/x

Answer 1

could you find inverse? ?
let you find inverse function as \(f(x)\)
composition means
\(f(g(x))\)
if your inverse is correct, then \(f(g(x)) = x\)

Answer 2

would the inverse be, x(x+3)

Answer 3

its (x-3)/x

or x - 3/x
?

Answer 4

(x-3)/x sorrry for not being clear

Answer 5

y = (x-3)/x

xy = x-3

xy - x = -3

x (y-1) = -3

x= -3/(y-1)

so your inverse function is
-3/(x-1)

did u get how i got the inverse ?

Answer 6

yes

Answer 7

what about using composition to justify the result?

Answer 8

if \(f(g(x))=x\)
then f and g are inverses of each other

g(x) = (x-3)/x
f(x) = -3/(x-1)

Answer 9

to get f(g(x)) , plug in the expression of g(x) in f(x)

Answer 10

wherever you see 'x' in f(x)
just replace it by
(x-3)/x

Answer 11

how would u simplify