A function \( f:R\to R \) defined as \( f(x)=x^{2}-4x+5 \) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Neither injective nor surjective
Completing the square,
\( \displaystyle f(x)=(x-2)^{2}+1 \)
Not injective: \( f(1)=f(3)=2 \), so two different inputs give the same output.
Not surjective: \( f(x)\ge 1 \), so the range is \( [1,\infty) \), not R; for example, 0 is never a value of f.