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Problem 47 Medium Difficulty
Express the function in the form $ f \circ g $.
$ v(t) = \sec (t^2) \tan (t^2) $
Answer
$$\text { Let } g(t)=t^{2} \text { and } f(t)=\sec t \tan t . \text { Then }(f \circ g)(t)=f(g(t))=f\left(t^{2}\right)=\sec \left(t^{2}\right) \tan \left(t^{2}\right)=v(t)$$.
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Top Calculus 3 Educators
Lily A.
Johns Hopkins University
Catherine R.
Missouri State University
Heather Z.
Oregon State University
Kristen K.
University of Michigan - Ann Arbor
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Video Transcript
here we have a function V of tea and we want to think of V A. T as a composition of functions f of G and another way to write that would be f of G of tea with parentheses. And looking at that notation, we can see that g of t is the inside function and f of tea is the outside function. So thinking about it that way we could see that the inside function could be t squared so we could let g of t equal t squared. And so the outside function would be C can't t tangent t And that way, if we found f of G, we could substitute t squared in for tea and we would get the original function v of tea.
Oregon State University
Top Calculus 3 Educators
Lily A.
Johns Hopkins University
Catherine R.
Missouri State University
Heather Z.
Oregon State University
Kristen K.
University of Michigan - Ann Arbor
