Final answer:
Assuming a typo correction, the function g(x) = 4 - (3/2)x is one-to-one and does have an inverse function. The inverse can be found by interchanging x and y and solving for y in the equation.
Step-by-step explanation:
To determine if the function g(x)=4-⅓/²x has an inverse function, we need to test if the function is one-to-one. A one-to-one function has exactly one output for every input and passes the horizontal line test, which means that no horizontal line intersects the graph of the function more than once. However, due to the typo in the original function, we can't perform this test accurately. Assuming the function was meant to be g(x) = 4 - (3/2)x, this function is a straight line, which is one-to-one, indicating that yes, it does have an inverse function. To find the inverse function, you would interchange the x and y and solve for y, a process that involves 'undoing' the original function.