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A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

$ g(x) = \sqrt[3]{x} $

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01:02

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

Oregon State University

Harvey Mudd College

University of Nottingham

Lectures

04:31

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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A function is given by a t…

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we're deciding whether or not this function is 1 to 1. So to do that, let's imagine the graph. The graph of the cube root of X looks like this now to be oneto. One means for every X value. There's only one Y value, and for every y value, there's only one X value, so it must pass the vertical line test and pass the horizontal line test. So checking the vertical line test pass a vertical line through it only passes through one point, not more than one. So that's a pass. And for the horizontal line test, pass a horizontal line through it cannot pass through more than one point. That's also a pass. So, yes, this one is 1 to 1.

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