AP EAMCET20228 Jul 2022Morning ShiftMathematicsFunctionsActual

If f: R R is defined as f(x)=x^2-2 x-3 then f is

Options

Aone-one but not onto
Bonto but not one-one
Cneither one-one nor onto
Da bijection

Correct answer

C. neither one-one nor onto

Step-by-step solution

f(x)=x^2-2 x-3 for one one Let f ( x ₁ )= f ( x ₂ ) aligned & x₁^2=2 x₁-3=x₂^2-2 x₂-3 & x₁^2-x₂^2-2 (x₁-x₂ )=0 & (x₁-x₂ ) [x₁+x₂-2 ]=0 & x₁=x₂ or x₁+x₂=2 aligned So, f(x) is not one-one for onto Let y=x^2-2 x-3=0 aligned & x^2-2 x-3-y=0 & x= 2 4-4(3+y) 2 =1 4+y & 4+y 0=y -4 & range =-4 codomain (R) aligned So, f(x) is not onto

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