JEE Main20246 Apr 2024Morning ShiftMathematicsFunctionsActual

The function f: R->R, f(x)= x^2+2 x-15 x^2-4 x+9 , x R is

Options

Aone-one but not onto.
Bboth one-one and onto.
Conto but not one-one.
Dneither one-one nor onto.

Correct answer

D. neither one-one nor onto.

Step-by-step solution

f(x)= (x+5)(x-3) x^2-4 x+9 aligned & Let g(x)=x^2-4 x+9 & D 0 for x R aligned [ array l f (-5)=0 f (3)=0 array . So, f ( x ) is many-one. again, aligned & y x^2-4 x y+9 y=x^2+2 x-15 & x^2(y-1)-2 x(2 y+1)+(9 y+15)=0 & for x R D 0 & D=4(2 y+1)^2-4(y-1)(9 y+15) 0 & 5 y^2+2 y+16 0 & (5 y-8)(y+2) 0 aligned

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