Is there any branch of constructing inverse function exist that is inverse of $n$ functions?

ntaraxq
2022-07-12
Answered

Is there any branch of constructing inverse function exist that is inverse of $n$ functions?

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Compute the inverse function of the following polynomial on $[0,1]$?

$f(x)=\alpha {x}^{3}-2\alpha {x}^{2}+(\alpha +1)x$

(where $\alpha $ is within $]0,3[$)

$f(x)=\alpha {x}^{3}-2\alpha {x}^{2}+(\alpha +1)x$

(where $\alpha $ is within $]0,3[$)

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Given

$$f(x)=2{x}^{2}+7x$$ and $$g(x)=3x+1$$, find $$(f\cdot g)(x)$$

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Find the inverse function if:

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$2{e}^{3x}=4{e}^{5x}$

asked 2022-06-04

Is it true that for $F:{\mathbb{R}}^{n}\to {\mathbb{R}}^{m}$ which has an inverse function ${F}^{-1}:{\mathbb{R}}^{m}\to {\mathbb{R}}^{n}$, says $F$ is diﬀerentiable at $a\in {\mathbb{R}}^{n}$ and ${F}^{-1}$ is diﬀerentiable at $b=F(a)\in {\mathbb{R}}^{m}$，then $m$ must be equal to $n$?

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Find the inverse function of

$f(x)=x-(2\sqrt{x})+1$

the domain of definition is $\phantom{\rule{thinmathspace}{0ex}}x\ge 0$

$f(x)=x-(2\sqrt{x})+1$

the domain of definition is $\phantom{\rule{thinmathspace}{0ex}}x\ge 0$