Final answer:
The inverse of the function f(x) = log(3)x is the exponential function g(x) = 3^x, obtained by switching the x and y in the original function and solving for y.
Step-by-step explanation:
The inverse of the equation f(x) = log(3)x can be found by swapping the x and y variables and solving for y. So, we get x = log(3)y. To find the equation, we need to isolate y. Start by exponentiating both sides using the base 3, which cancels out the logarithm. To find the inverse of the function f(x) = log(3)x, you need to interchange the roles of the x and y variables and then solve for y. Start by letting y = log(3)x, which means 3^y = x. Then by interchanging x and y, you would have 3^x = y. Therefore, the inverse function is g(x) = 3^x.