I want to prove that this function $f(x)=\frac{x}{\cos x}$ from $(-1,1)$ to $\mathbb R$ is bijective? whether or not has an inverse differentiable? I know that this function is injective and surjective so is bijective, but I am not able to find its inverse. thanks.
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Do you mean from $\left(-\frac\pi2,\frac\pi2\right)$ to $\mathbb{R}$? – robjohn Dec 04 '17 at 16:37
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yes, I want to find its inverse function. – zeinab Dec 04 '17 at 16:42
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I don't think there is a special function for the inverse, even the cardinal sinus which is more popular doesn't have one. – zwim Dec 04 '17 at 17:07
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what about its inverse differentiable? – zeinab Dec 04 '17 at 19:23