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Express the function in the form $f \circ g \circ h$.$H(x) = \sqrt[8]{2 + \mid x \mid}$

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Lily A.

Johns Hopkins University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

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Video Transcript

here we see the function capital H of X, and we want to break that down into a composition f of G of h. Another way to write that is with parentheses. F of G of h of x. Okay, so that shows us that H of X is going to be the innermost function. So if we look back at capital age, it looks like absolute value of X could be the innermost function. So let's let little h of X equal the absolute value of X. Now the question is, what is it inside of? Because that has to be inside of G. So let's figure out g of X. If we let g of X equal to plus X, then it looks like a chav X was put in there in the place of X, so that G of h of X would be to plus the absolute value of X. Now. Thirdly, we want to find the outermost function F. So what is surrounding G of h of X? It's being surrounded by the eighth route. So if f of X is the eighth route of X and if we substitute G of h of X into it, then we're substituting two plus absolute value backs into the eighth route and we do get capital age. That's what we were hoping for.

Oregon State University
Lily A.

Johns Hopkins University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Lectures

Join Bootcamp