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