I will go over three examples in this tutorial showing how to determine algebraically the inverse of an exponential function. But before you take a look at the worked examples, I suggest that you review the suggested steps below first in order to have a good grasp of the general procedure.

The inverse function of an exponential function [latex]f(x)=r^x[/latex], is found by switching the input [latex]x[/latex] and output [latex]y[/latex]. We start by writing [latex]y[/latex] for [latex]f(x)[/latex] then switch [latex]x[/latex] and [latex]y[/latex] to get the inverse function:

2022年11月16日 · Here is a set of practice problems to accompany the Inverse Functions section of the Graphing and Functions chapter of the notes for Paul Dawkins Algebra course at Lamar University.

Example 1: List the domain and range of the function ( ) = log2( ). Then find its inverse function −1( ) and list its domain and range. When finding the inverse of an exponential or logarithmic function, we are basically just converting from one form to the other.

2.10.A Construct representations of the inverse of an exponential function with an initial value of 1.

2024年9月24日 · Another example of inverse pair is the exponential and logarithm function, both are inverse of each other. For an exponential function f(x) = a x , its inverse is given by logarithm i.e., log a x, and vice versa.

The inverse function of exponential functions are called logarithms. Logarithmic functions have different bases depending on the base of the original exponential function. y = 2x would be y=log2x. y = log ⁡ 2 x. y=\log_2 x. y = log2 x. y = loge x but y=lnx. y = ln ⁡ x. y=\ln x. y = lnx. e ”.

2024年2月1日 · To find the inverse of an exponential function, I first replace the function notation ( f (x) ) with ( y ). This small change sets me up to address the function more like an equation involving ( y ) and ( x ). Next, I swap the roles of ( x ) and ( y ); where ( x ) was the input and ( y ) the output, they now switch positions.

Check the following example to understand the inverse exponential function and logarithmic function in detail. Also, get more insights of how to solve similar questions and thus, develop problem-solving skills.

2023年11月13日 · The inverse of an exponential function is denoted as ‘f^(-1)(x)’, where ‘f(x)’ is the original exponential function. The inverse function allows us to find the input value for a given output value, which is the reverse of what the original exponential function accomplishes.