By using the definition, we will see that the inverse of y = 11^x is:
g(x) = log₁₁(x)
What is an inverse function?
Two functions f(x) and g(x) are inverses if:
f( g(x)) =x
g(f(x)) = x
Now, we want to find the inverse of:
y = 11^x
So we need to apply a function such that:
g(y) = x
Starting with a natural logarithm, we get:
Ln(11^x) = Ln(11)*x
Now we could divide by ln(11).
Then, if we define:
g(x) = ln(x)/ln(11) = log₁₁(x)
We will have that g(x) is the inverse of y = 11^x
If you want to learn more about inverses, you can read:
https://brainly.com/question/12220962
