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The graph of $ f $ is given.(a) Why is $ f $ one-to-one?(b) What are the domain and range of $ f^{-1} $ ?(c) What is the value of $ f^{-1} (2) $?(d) Estimate the value of $ f^{-1} (0) $.

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02:40

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Missouri State University

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

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In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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all right. So here we have a rough sketch of the graph of F, and it's 1 to 1 because every X value has only one y value and every y value has only one X value. And graphically, we can say it passes the horizontal line test as well as a vertical line test. Okay, now we went to find the domain and range of F inverse. So first of all, let's find the domain and range of F. So the domain of F the X values that goes through our negative 3 to 3 on the range of death, the Y values that goes through our negative 123 So the domain of F inverse will be the range of F, and the range of FM burst will be the domain of F. So we're going to switch these and the domain of F inverse will be from negative 123 and the range will be from negative 3 to 3. When you have an inverse outputs become inputs, inputs become outputs. All right. Now let's find the value of f inverse of to so effin versus to let's say it equals X, then that means that f of X equals two, the output of X inverse will be the inverse will be the input of F inputs and outputs are switched. So what? X value appears to have a Y value of two. Looking at the graph, it looks like X equals zero has a Y value of two. So f inverse of two is zero. And finally, let's estimate the value of F inverse of zero. So similarly, let's just say that it's X, so that means that f of X equals zero. So we're estimating the value of the point where there's a wide coordinate of zero on the graph. Now you really should look at the graph in the book, not my graph, because mine is just a rough sketch. And if you look at the graph in the book, you see that it passes through a height of zero at about negative 1.5 negative 1.6 somewhere in there, so f inverse of zero is approximately negative. 1.6

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