# Continuity of two functions

Well, I am little confused about these problems; I need some help:

1. Show that the equation $$4x-3\cos(x)=1-2t\cos(t)$$ defines a unique continuous function on any $[a,b].$
2. same problem for the equation $$\tan^{-1}(t)+x+\tan^{-1}(xt)=0,$$ where $-1<a<0<b$
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To determine whether they're functions or not, we need to know which variable is independent. – Patrick Mar 31 '12 at 13:37