Question

What is the inverse function for $f(x)=3 e^{x-1}+4 ?$

   What is the inverse function for $f(x)=3 e^{x-1}+4 ?$

Algebra and Trigonometry

Algebra and Trigonometry

Michael Sullivan 11th Edition

Chapter 11, Problem 93

Instant Answer

Solved by Expert James Kiss

09/29/2021

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Step 1: First, we start with the given function $f(x)=3e^{x-1}+4$. Show more…

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What is the inverse function for $f(x)=3 e^{x-1}+4 ?$

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Key Concepts

Logarithmic Functions

Logarithmic functions are the inverses of exponential functions. They are used to 'undo' the effect of an exponential, particularly when solving for variables in the exponent. The natural logarithm, ln, is commonly used when working with exponentials with base e, enabling the equation to be linearized.

Exponential Functions

Exponential functions involve raising a constant base, typically e, to a function of the variable. These functions exhibit rapid growth or decay and often include transformations such as shifts and scaling. Understanding their structure is key to performing operations like finding inverses.

Inverse Functions

An inverse function reverses the effect of the original function, mapping outputs back to their corresponding inputs. To find an inverse, you swap the roles of the dependent and independent variables and then solve for the new dependent variable. This process requires that the original function is one-to-one so that each input has a unique output.

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