Author Topic: A few questions from my hw (Read 839 times) Tweet Share

ejf8888 · « **on:** March 16, 2009, 03:52:55 pm »

Hi,

There are two questions on my hw sheet that im not sure how to go about working them out. One I have tried to find an answer sure, but the other i dont know where to start.

Any help that anyone can give would be greatly appreciated!

1) What is the domain of Cos^-1modulus of x (sorry not sure how to write it on the comp)

I got [-1, 1] but im really not sure

2) Evaluate Tan ^-14 - Tan^-1(3/5)

I have no idea for this one.

Thankyou in advance for any help!

TrueTears · « **Reply #1 on:** March 16, 2009, 06:09:00 pm »

For question 1, you might want to try split the function up into a composite function

eg, Let $cos^{-1}(x) = f(x) and |x| = g(x)$

so $f o g = cos^{-1}(|x|)$

now using knowledge of composite functions, for $f o g$ to be defined, $ran g \subset dom f$

$ran g = [0,\infty)$ and $dom f = [-1,1]$

so for $f o g$ to exist we must restrict the ran g to at least [0,1] and for this to occur dom g must be restricted to [-1,1]

so now we also know that $dom f o g = dom g$ (using knowledge of composite functions)

hence $dom f o g = dom cos^{-1}(|x|) = dom g = [-1,1]$

Hope that helps

kamil9876 · « **Reply #2 on:** March 16, 2009, 07:43:24 pm »

2.) $\arctan 4$ and $\arctan \frac{3}{5}$ are angles. So the difference of these two expressions is the difference of two angles, hence difference of angels should come to mind:

$\tan(\arctan (4) - \arctan (3/5))=\frac{\tan(\arctan (4)) - \tan(\arctan(3/5))}{1+\tan(\arctan(4))\tan(\arctan (3/5))}$

$= \frac{4 - 3/5}{1 + 12/5}$

$= \frac{20-3}{5+12}$

$= \frac{17}{17}$

rest is trivial...

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Author Topic: A few questions from my hw (Read 839 times) Tweet Share

ejf8888

A few questions from my hw

TrueTears

Re: A few questions from my hw

kamil9876

Re: A few questions from my hw

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