Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_functions
Class 12 Maths · Relations And Functions · Mcq Single Correct #78
Let \(f:\mathbb R\to\mathbb R\), \(f(x)=2x^3+2x^2+300x+5\sin x\). Then \(f\) is
✅ Step-by-Step Solution
Final Answer: Option (A): One-one onto
- \(f\prime(x)=6x^2+4x+300+5\cos x\ge6(x+1/3)^2+883/3>0\), so the function is strictly increasing. Its cubic leading term gives limits \(-\infty\) and \(+\infty\) at the two ends; continuity gives surjectivity.
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