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tmua.me Medium Set A Paper 2 · Q12

Paper 2Functions & graphs

For a real constant kk, the function ff is defined for all real xx by

f(x)=x3+3x2+kx.f(x)=x^3+3x^2+kx.

Consider the statements

  • PP: k≥3k\geq3.
  • QQ: For all real numbers uu and vv, if f(u)=f(v)f(u)=f(v) then u=vu=v.

Which of the following is correct?

APP is both necessary and sufficient for QQ
BPP is sufficient but not necessary for QQ
CPP is neither necessary nor sufficient for QQ
DPP is necessary but not sufficient for QQ

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