Bahar Tehranipoor

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Find the inverse of the functions. $f(x)=\frac{3}{x-4}$

   Find the inverse of the functions.
$f(x)=\frac{3}{x-4}$

Precalculus

Jay Abramson 1st Edition

Chapter 3, Problem 566

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Solved by Expert Bahar Tehranipoor

07/25/2019

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So, we have $y = \frac{3}{x-4}$. Show more…

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Find the inverse of the functions. $f(x)=\frac{3}{x-4}$

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Key Concepts

Inverse Function

An inverse function is a function that reverses the effect of the original function, meaning that if the original function f maps an element x to y, then its inverse f?¹ maps y back to x. The process of finding an inverse involves swapping the roles of the independent and dependent variables and solving for the new dependent variable.

Algebraic Manipulation

Finding the inverse of a function typically requires a series of algebraic steps: replacing f(x) with y; swapping x and y; and then solving the resulting equation for y. This procedure involves operations such as cross multiplying, isolating the variable, and simplifying.

Domain and Range

The domain and range of a function and its inverse are interchanged. Understanding the constraints on the original function, including any restrictions or points of discontinuity, is crucial when determining the valid input values for the inverse function.

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