Use the given relationsfandgto find (a) f · g (b) f/g (f over g) (c) f∘g (d)g∘f

f(x)=Cos(x) g(x)=Csc(x)Tan(x)

can i see the steps on how to on these?

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- Jul 20th 2010, 03:23 PM #1

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- Jul 20th 2010, 03:36 PM #2

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- Jul 20th 2010, 03:42 PM #3

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- Jul 20th 2010, 03:46 PM #4
I'll do (a)...

$\displaystyle \begin{aligned}

f \cdot g &= (cos \, x)(csc \, x)(tan \, x) \\

&= (cos \, x)\left( \frac{1}{sin \, x} \right) \left( \frac{sin \, x}{cos \, x} \right) \\

&= 1

\end{aligned}$

But this is not the same as your linear function y = 1. $\displaystyle f \cdot g$ is going to look like a horizontal line with some "holes". The domain of f(x) = cos(x) is all real numbers, but the domain of g(x) = csc(x)tan(x) is all reals except multiples of pi/2. So the domain of $\displaystyle f \cdot g$ is the intersection of the two domains, or all reals except multiples of pi/2.

- Jul 20th 2010, 03:53 PM #5

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- Jul 20th 2010, 11:33 PM #6