Question

consider the graph of the polynomial function, g(x), where the domain is all real numbers, and the range is all real numbers. what is the domain of $g^{-1}(x)$? \bigcirc all real numbers \bigcirc only integers \bigcirc only integers between -10 and 10, inclusively \bigcirc only real numbers between -10 and 10, inclusively

Explanation:

Step1: Recall Inverse Function Domain

The domain of an inverse function \( g^{-1}(x) \) is the range of the original function \( g(x) \).

Step2: Analyze Original Function \( g(x) \)

The original function \( g(x) \) is a polynomial (from the graph, it's a continuous curve). For polynomial functions, the range is all real numbers (since polynomials are continuous and extend to \( \pm\infty \) as \( x \to \pm\infty \), covering all real \( y \)-values).

Step3: Determine Domain of \( g^{-1}(x) \)

Since the range of \( g(x) \) is all real numbers, the domain of \( g^{-1}(x) \) (which is the range of \( g(x) \)) must also be all real numbers.

Answer:

all real numbers