Inverse trig domain

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September 9th 2010, 05:32 AM
Stroodle

Inverse trig domain

Hi,

How would I go about finding the implied domain of $f(x)=1+cos^{-1}(3x)$ ?

Thanks for your help!
September 9th 2010, 06:41 AM
Failure

Quote:

Originally Posted by Stroodle

Hi,

How would I go about finding the implied domain of $f(x)=1+cos^{-1}(3x)$ ?

First I would scan for terms that might have a limited domain. The constant part 1 is not a problem, nor is $3x$ , but the domain of $\cos^{-1}$ is $[-1;+1]$ .
So the (implied) domain of your function is the set $\{x\in \mathbb{R} : 3x\in [-1;+1]\}=[-1/3;+1/3]$

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