Question

What is the inverse of the logarithmic function f(x) = log9x?

Answer 1

f –1(x) = 9x

if youre taking this on edg the next question is

How can you use a point on the graph of f –1(x) = 9x to determine a point on the graph of f(x) = log9x? answer: switch the x and y coordiantes

Answer 2

The domain of the function converted into the range of the inverse function and the range of the inverse function are converted into the domain. For finding the inverse, the variables are interchanged by the functional value. The inverse of $f(x)=\log 9x$ is $\dfrac{10^x}{9}$.

The given function is $f(x)=\log 9x$

Let us assumed the functional value be $y$.

Now, Solve the function for $x$.

$\begin{aligned}y&=\log9x\\10^y&=9x\\x&=\dfrac{10^y}{9} \end{aligned}$

Now, for the inverse function, the value of x should be the functional value.

Thus, $f^{-1}(x)=\dfrac{10^x}{9}$

To know more about inverse function, please refer to the link:

https://brainly.com/question/15912209