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Determine the equation of the inverse function.$$f(x)=2 x+1$$

$f^{-1}(x)=\frac{x-1}{2}$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

Missouri State University

McMaster University

Harvey Mudd College

Lectures

00:25

Find the inverse function …

00:35

Finding Inverse Functions …

00:16

Find the inverse of each f…

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01:20

So if we want to find the inverse of this function, uh, first thing we should do is make sure that it is 1 to 1. And so if we were to come over here and just take the derivative of this, we didn't know what to which is strictly larger than zero. So that implies this is always increasing, which is one of the type of functions that we know is always want to one. And now, at this point, what we can do is go ahead, replace ffx will fly and then interchange the x and Y and then solve for y. So we have X is equal to two y plus one. So subtract one over X minus. One is equal to two. Why divide by two? So we have X minus 1/2 is equal to y. And so then this is going to be our inverse

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