Which statement about y = x2 − x3 is true?a.It is not a function.b.It is an even function.c.It is neither an odd nor an even function.d.It is an odd function.
Accepted Solution
A:
ANSWERc.It is neither an odd nor an even function.EXPLANATIONThe given function is [tex]y = f(x) = {x}^{2} - {x}^{3} [/tex]If this function is odd, then f(-a)=-f(a).[tex]f( - a) = {( - a)}^{2} - {( - a)}^{3} [/tex][tex]f( - a) = {( a)}^{2} + {( a)}^{3} [/tex]Now ,[tex]f( a) = {( a)}^{2} - {( a)}^{3} [/tex][tex] - f( a) = - {( a)}^{2} + {( a)}^{3}[/tex]Since[tex]f( - a) \ne - f(a)[/tex]The function is not odd.Also if the function is even, then [tex]f( a) = f( - a)[/tex]Since [tex]f( a) \ne f( - a)[/tex]the function is not even.Hence the function is neither even nor odd.