If g : [ − 1 , 1 ] → R is a function and the area of the equilateral triangle with two of its vertices at ( 0 , 0 ) and ( x , g ( x )) is 4 3 , then g ( x ) =

Question

If g : [ − 1 , 1 ] → R is a function and the area of the equilateral triangle with two of its vertices at ( 0 , 0 ) and ( x , g ( x )) is 4 3 ​ ​ , then g ( x ) =

TestHub · Accepted Answer

If a = length of a side = ( x − 0 ) 2 + ( g ( x ) − 0 ) 2 ​ = x 2 + g 2 ( x ) ​ Area of an equilateral triangle = 4 3 ​ ​ a 2 = 4 3 ​ ​ ⇒ x 2 + g 2 ( x ) = 1 ⇒ g ( x ) = + 1 − x 2 ​

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