Let g(x) be a function defined on [-1, 1]. If the area of the equilateral triangle with two of its vertices at (0, 0) and (x,g(x)) is 3/4, then

Side of the triangle with vertices (0, 0) and x,gx is a x2+gx2. Area of equilateral triangle, whose side a is 34a2.∴34x2+gx2=34⇒x2+gx2=1⇒ g(x)=±1−x2. Thus g(x)=1−x2