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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
$f: R \rightarrow R, f(x)=x^2+3 x+4$ is __________
  • A
    one-one and onto
  • B
    one-one and not onto
  • ✓
    many-one and not onto
  • D
    many-one and not onto
✓

Answer

Correct option: C.
many-one and not onto
(C)
$f (x)=x^2+3 x+4$
$=x^2+3 x+\frac{9}{4}-\frac{9}{4}+4$
$=\left(x^2+3 x+\frac{9}{4}\right)+\frac{7}{4}$
$=\left(x+\frac{3}{2}\right)^2+\frac{7}{4}$
Hence, $f$ is many-one and not onto

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