Mathematics, 26.06.2019 12:30 miagiancarlo
what would this be? the cool equation is y=2-x^3. i'm doing inverse functions.
Answers: 1
, and you're asked to find the inverse function 
. To do this, swap 
and 
, then solve for ![x=2-y^3\implies y^3=2-x\implies y=(2-x)^{1/3}=\sqrt[3]{2-x}](/tpl/images/0019/4581/eccdf.png)
![y^{-1}(x)=\sqrt[3]{2-x}](/tpl/images/0019/4581/9f1b2.png)
![y(y^{-1}(x))=y(\sqrt[3]{2-x})=2-(\sqrt[3]{2-x})^3=2-(2-x)=x](/tpl/images/0019/4581/b2ffb.png)
![y^{-1}(y(x))=y^{-1}(2-x^3)=\sqrt[3]{2-(2-x^3)}=\sqrt[3]{x^3}=x](/tpl/images/0019/4581/7405c.png)
(the real-valued square root) is only defined as long as 
. So 
is defined as long as 
, or 
, or equivalently 
. Under this condition, we could write
. Then 
. But we get the same result if 
, since 
. There are two possible values of 
, so to capture both of them, we take 
, the absolute value of 
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[tex] \sqrt{ - x ^{3} } [/tex]what would this be? the cool equation is y=2-x^3. i'm doing inverse f...
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