Consider 2 functions f(x), g(x) that is defined on the interval [0, \infty) where
f(x)=x^3+x^2+x+2
g(x)=2f^{-1}(x)-1
Find the value of \(g(0) + g(3)\)
+9674 g(0) is not well-defined since f^{-1}(0) does not exist in [0, \infty), i.e., there is no x \in [0, \infty) such that f(x) = 0.
Proof:
Since \(x\in [0, \infty)\), \(x^3, x^2, x\) are all nonnegative.
Then \(f(x) = x^3 + x^2 + x + 2 \geq 0 + 0 + 0 + 2 = 2 > 0\) for any \(x\in [0, \infty)\).
Then we have \(f(x) > 0\) for any \(x\in [0, \infty)\).
This implies there are no \(x\in [0, \infty)\) such that \(f(x) = 0\).
Therefore, we cannot find the value of \(g(0) + g(3)\).
