Final answer:
The inverse function g will undo the action of function f. Since f(4) = 6, the inverse g will turn 6 back to 4. Therefore, g(6) = 4.
Step-by-step explanation:
To find the value of g(6) when g is the inverse function of f, and given that f(6) = 9 and f(4) = 6, we must use the definition of inverse functions.
An inverse function reverses the action of the original function. That is, if f(x) = y, then g(y) = x. In this case, since f(6) = 9, the inverse function g would now turn 9 back into 6.
Therefore, g(9) = 6.
However, we need to find g(6). Looking at the second piece of information given, f(4) = 6, tells us that in the inverse function, 6 would be turned back into 4.
Hence, g(6) = 4.