Question

Find f(x) and g(x) so that the function can be described as y = f(g(x)). y = 3/ square root of 3x + 4

Answer 1

Well, your equation y=3/SQRT(3x+4) should be rationalized, but that's not what you want.

If f(x) = 3/SQRT(x+4) and g(x) = 3x

f(g(x)) then = 3/SQRT(3x+4), but rationalizing this = 3SQRT(3x+4)/(3x+4)

Answer 2

g(x) = 3x + 4

and f(x) =
`(3)/(√(x))`

Explanation:

The function
`y=(3)/(√(3x+4))`

has two possible f(x) and g(x).

If g(x) = 3x + 4

and f(x) =
`(3)/(√(x))`

OR, If g(x) =
`√(3x+4)}`

and f(x) =
`(3)/(x)`.

Further, f(g(x)) is the symbol of composition.