# Inverse trig domain

• September 9th 2010, 06:32 AM
Stroodle
Inverse trig domain
Hi,

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

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 $\{x\in \mathbb{R} : 3x\in [-1;+1]\}=[-1/3;+1/3]$