The inverse of the logarithmic function is the exponential function. For the logarithmic function f(x) = log9(x), the base of the log is 9. To find the inverse, we can set up the relationship:
Let y = log9(x). This implies that:
9y = x
Now, to express the inverse function, we will switch the roles of x and y. Thus, we write:
f-1(x) = 9x
This means that the inverse function f-1(x) takes an input of x and returns 9x, which is an exponential function with base 9.
In summary, the inverse of the logarithmic function f(x) = log9(x) is f-1(x) = 9x.