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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
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up vote 0 down vote accepted

you may want to show that they are differentiable, and hence continuous.

Not sure what level of rigour the problem requires, if it is epsilon-delta rigourousness, then it is hard work. Otherwise, you can state that products of continuous functions are continuous, etc..

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