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Assume that $ f $ is a one-to-one function.
(a) If $ f(6) = 17 $ , what is $ f^{-1} (17) $?(a) If $ f^{-1} (3) = 2 $ , what is $ f(2) $?
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01:14
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
Idaho State University
Lectures
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A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.
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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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Assume that $ f $ is a one…
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Assume that $f$ is a one-t…
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Assume that the function $…
in this problem. We're talking about inverse functions and particularly coordinate pairs that would fall on inverse functions. And one of the features of inverse functions is that if F of X contains the point a B, then f inverse of X will contain the point B A. So the coordinates switch places a and B switch. So if you have the 0.6 17 as a point on f of X, you're going to have the 170.0.17 6 as a point on F in verse. So that tells us that F inverse of 17 will be six. Similarly, if you have the 0.32 on f inverse, you're going to have the 0.23 on F and so f of two will be three.
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