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Let $f(x)$ be a continues function for all $x$, and $|f(x)|\le7$ for all $x$.

Prove the equation $2x+f(x)=3$ has one solution.

I think the intermediate value theorem is key in this, but I'm not sure of the proper usage.

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    @Nameless I assume so too, but I was interested in whether the question had been correctly posed (there might be a monotonicity criterion missed) and in pointing out an ambiguity in the way the question is asked, which might help the person who asked the question to formulate their thoughts more clearly.2012-12-29

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Hint: Let $g(x)=f(x)+2x-3$. Then $g(-2)$ and $g(5)$ are...

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    @pie Sure. My advice: Just concentrate on what the problem is, what you want to show and never lose sight of that.2012-12-29