SOLUTION: If g(x) is the inverse of f(x)=√(x^3) + 1 . which of the following is on g(x)? A). (4,9) B). (9,4)

Algebra ->  Inverses -> SOLUTION: If g(x) is the inverse of f(x)=√(x^3) + 1 . which of the following is on g(x)? A). (4,9) B). (9,4)       Log On


   

Question 1017128: If g(x) is the inverse of f(x)=√(x^3) + 1 .
which of the following is on g(x)?
A). (4,9)
B). (9,4)
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
The easiest way would be to plug in both points after finding the inverse.

y = sqrt(x^3) + 1
y - 1 = sqrt(x^3)
(y - 1)^2 = x^3
(y - 1)^(2/3) = x

g^(-1)(x) = cbrt((x - 1)^2)

g^(-1)(4) = cbrt(3^2) = cbrt(9)
g^(-1)(9) = cbrt(8^2) = 4

The point (9, 4) is on g^(-1)(x).