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Numerade Educator

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Problem 48 Medium Difficulty

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

$ u(t) = \dfrac {\tan t}{1 + \tan t} $

Answer

$g(t)=\tan t$ and $f(t)=\frac{t}{1+t}$

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Video Transcript

Here's the function U of T and we want to think of the function as a composition f of G and another way to write that would be with parentheses, f of g of t. So, looking at it that way we can tell that G would be the inside function and f would be the outside function. So when we look back at V A. T what appears to be the inside function? What we can see that tangent t is on the inside of something else in two places. So we could say that GFT is tangent e So what is it inside of? So what is fft? Well, we would have to have tea on the top to place the g of t in there and we would have to have one plus t on the bottom to place a tangent of T in there, so that would be our FFT. So f of G would give us the original function