If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^3+6x^2+12x+9), which statement about the one-one nature of (f) is correct?

Correct answer: It is one-one

Step 1: The function can be written as (f(x)=(x+2)^3+1). Step 2: A cubic form is strictly increasing on the whole real domain, so two different (x)-values cannot have the same image. Step 3: In such questions, first try to identify a perfect cubic form.