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Express the function in the form $ f \circ g $. …

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Problem 42 Medium Difficulty

Find $ f \circ g \circ h $.

$ f(x) = \tan x $ , $ g(x) = \dfrac{x}{x - 1} $ , $ h(x) = \sqrt[3]{x} $


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Jeffrey Payo

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Calculus: Early Transcendentals

Chapter 1

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Multivariate Functions - Intro

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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12:15

Partial Derivatives - Overview

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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Find $f \circ g \circ h$

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Video Transcript

here we have the functions F, g and H, and we're going to find the composition f of G of h. Another way to write that is with parentheses, f of G of h of X. And when we read it that way we can see that H is the inside function. It's going to be substituted into G. So we're going to take the cube root of X and we're going to substituted into G. In both places, we see an X that gives us G of h of X. So G of h of X is the cube root of X over the cube root of X minus one. So that whole thing goes inside of death. So we take that whole thing and we substituted in to the F function in place of X. And that's going to result in the tangent of that Hubert of X, over the cube root of X minus one

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Calculus: Early Transcendentals

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Related Topics

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Video Thumbnail

04:31

Multivariate Functions - Intro

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.

Video Thumbnail

12:15

Partial Derivatives - Overview

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.

Join Course
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