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By using the Intermediate value theorem.

Show that f is continuos on $[-1,1]$, then there exist n in the natural numbers such that the equation $f(x) + n = n(e^x)$ has a solution in $[-1,1]$.

I'm having trouble solving this problem. Any help is appreciated.

mark
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Edelon Grech
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1 Answers1

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Define $g(x) := f(x) + n - n(e^x)$. Then $g$ is continuous and we have $g(-1) = f(-1) + n - \frac{n}{e}$ and $g(1) = f(1) + n - ne$. Can you finish it from here?

Shuster
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