Question

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

Answer 1

Answer: The inverse of the logarithmic function will be

$f^{-1}(x)=9^x$

Step-by-step explanation:

Since we have given that

$f(x)=\log_9(x)$

Replace f(x) with y.

$y=\log_9(x)$

Now, interchanging with variables:

$x=\log_9(y)$

$\implies y=9^x$

Now, again put y = f(x).

So, it becomes,

$f(x)=9^x$

Hence, the inverse of the logarithmic function will be

$f^{-1}(x)=9^x$

Answer 2

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