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Solve equation with $\arccos$ and sqrt

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surjectivity of a piece-wise function defined as follows

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inverse relation need not to be a function.

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#functions #relations #inverse-function
66
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prove that $f^{-1} = f*$ as follow

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40
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Show that $f^*:B \to A$ is a function iff $f$ is bijective as follows.

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374
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Inverse of a function with square root

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198
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Inverse of function of projective space $\mathbb{R}P^1$ in $\mathbb{S}^1$?

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45
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Inverse sine simplifying problem

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563
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$\arctan x$ vs $1/\tan x$

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#trigonometry #notation #inverse-function
49
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Continuous and invertible function

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Solve Surface Area Formula For Radius

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#quadratics #inverse-function
48
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Explaining an incorrect solution involving derivative of an inverse.

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#calculus #derivatives #education #inverse-function #inverse-function-theorem
74
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If $\lim_{x \to a} f\left(x\right) = L$ then does $\lim_{x \to L} f^{-1}\left(x\right) = a$

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#calculus #limits #inverse-function
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If $f:R\to [-\frac{\pi}{4}, \frac{\pi}{2})$, $f(x)=\tan^{-1} (x^4-x^2 -\frac 74 +\tan^{-1} \alpha)$, find $\alpha$

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105
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Evaluate $\sin (\cot ^{-1} (1+x)) = \cos (\tan^{-1} (x))$

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