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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
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    To determine whether they're functions or not, we need to know which variable is independent.2012-03-31

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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..