Why is the range not all real numbers for this function: f(x)=sin^-1(x)

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Why is the range not all real numbers for this function: f(x)=sin^-1(x)

Mathematics
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the domain is restricted so that it is a function.... hence the restriction on the range
wait can you explain in it in a more thorough way

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well do you know the definition of a function...?
a relationship that involves one or more variables
ok... so here is the graph |dw:1438027719063:dw| a simple test for a function is called the vertical line test, hopefully you have know it. but a relationship is a function is a vertical line only cuts the curve in 1 place if you curve us continued |dw:1438027846892:dw| the curve when extended to pi and -pi fails the vertical line test so its not a function....

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