Question

If f(x) = x⁵ - 3x + 2 and g(x) = f^(-1)(x), find (g^(-1))(2):

a) 0
b) 1
c) 2
d) 3

Answer 1

To find (g^(-1))(2), find the inverse of g(x) and substitute x=2 into the inverse function, which gives (g^(-1))(2) = 0.

Step-by-step explanation:

To find (g^(-1))(2), we need to find the inverse of g(x) and then substitute x = 2 into the inverse function.

1. First, let's find the inverse of g(x). Since g(x) = f^(-1)(x), we know that f(g(x)) = x.
2. Substitute g(x) into f(x), we get: f(g(x)) = g(x)^5 - 3g(x) + 2 = x.
3. Next, let's solve this equation for g(x) using algebraic operations, so that we get: g(x) = ((x - 2) / x)^(1/5).
4. Finally, substitute x = 2 into g(x) to find (g^(-1))(2). We get: (g^(-1))(2) = ((2 - 2) / 2)^(1/5) = 0^(1/5) = 0.