Question

How do you find the inverse function of an exponential function, and how does the base of the exponential function relate to the inverse function?

a) The inverse of an exponential function is found by switching the x and y coordinates and changing the base to its reciprocal.
b) To find the inverse of an exponential function, you take the logarithm of both sides, and the base of the exponential function becomes the base of the logarithm in the inverse function.
c) The inverse of an exponential function has the same base as the original function, but the exponent becomes the coefficient of the inverse function.
d) The base of the exponential function is not relevant to finding its inverse; it depends on the form of the original function.

Answer 1

To find the inverse of an exponential function, you take the logarithm of both sides, and the base of the exponential function becomes the base of the logarithm in the inverse function.

Step-by-step explanation:

To find the inverse of an exponential function, you take the logarithm of both sides, and the base of the exponential function becomes the base of the logarithm in the inverse function. This means that option b) is the correct answer. Let's take an example to illustrate this:

If we have the exponential function y = 2x, the inverse function will be y = log2(x). In this case, the base of the exponential function is 2, and it becomes the base of the logarithm in the inverse function. The exponent x in the exponential function becomes the argument of the logarithm in the inverse function.

Therefore, the inverse function of an exponential function is found by taking the logarithm of both sides, and the base of the exponential function becomes the base of the logarithm in the inverse function.