Questions: What is the domain of g^-1(x)? State in interval notation. dom(g^-1(x))= What is the range of g^-1(x)? State in interval notation. ran(g^-1(x))=

Domain of \( g^{-1}(x) \): \([-5, 3]\)
Range of \( g^{-1}(x) \): \([-4, 2]\)

Transcript text: What is the domain of $g^{-1}(x)$ ? State in interval notation. $\operatorname{dom}\left(g^{-1}(x)\right)=$ $\square$ What is the range of $g^{-1}(x)$ ? State in interval notation. $\operatorname{ran}\left(g^{-1}(x)\right):$ $\square$

Solution

Solution Steps

Step 1: Identify the domain of $ g(x) $

The domain of $ g(x) $ is the set of all possible input values (x-values) for which the function is defined. From the graph, $ g(x) $ is defined for $ x $ in the interval $[-4, 2]$.

Step 2: Determine the range of $ g(x) $

The range of $ g(x) $ is the set of all possible output values (y-values) that $ g(x) $ can take. From the graph, $ g(x) $ takes values from $[-5, 3]$.

Step 3: State the domain and range of $ g^{-1}(x) $

For the inverse function $ g^{-1}(x) $: