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Determine the equation of the inverse function.$$f(x)=\sqrt{2 x+3}$$

$f^{-1}(x)=\frac{x^{2}-3}{2}, x \geq 0$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:20

Finding Inverse Functions …

00:35

Find the inverse of the fu…

01:52

Find the inverse function …

01:00

Find a formula for the inv…

01:30

01:50

01:37

Find the inverse of each f…

00:56

01:16

01:19

Use algebra to find the in…

So if we want to find the inverse of this function, the first thing we should do because notice how the range of this isn't going to be all real numbers. Um, but the inverse we should get should be like a square or quadratic. So we know quadrants are defined for all real numbers. What we should do is first figure out. Well, what is the range of f going to be? Well, so this is the square root function. Um, and the inside when we multiply or divide by anything and Adams attracted, just changes the horizontal component. This is just going to be 02 infinity. So that tells us our domain for our inverse is going to be the same. So it will be 02 infinity as well, But yeah, we just need to kind of keep that in mind. So let's come over here and start solving for it. So it would be why here we square each side so we get why, actually, first we interchange X and Y B X is equal to the square root of two y plus three. We square each side, so X squared is equal to two y plus three, subtract the three and then divide each side by two. So we get that. That is equal to why, Um And then that would just be our inverse. Oh, and also, given that our domain is going to be X greater than or equal to zero. So that is something important to make note of, because otherwise they could also be the other side. Or it could just be all real numbers. Uh, so be sure to actually say X is greater than or equal to zero.

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