Given f(x)=x3+5x+1 Now f′(x)=3x2+5>0,∀x∈R ∴f(x) is strictly increasing function ∴ It is one-one Clearly, f(x) is a continuous function and also increasing on R, Ltx→−∞f(x)=−∞ and Ltx→∞f(x)=∞ ∴f(x) takes every value between −∞ and ∞. Thus, f(x) is onto function.
For real x, let f(x)=x^3+5 x+1, then
JEE Main 2009 — Mathematics Algebra
2009mcqeasy
For real x, let f(x)=x3+5x+1, then
Official previous-year question
Held on 30 Apr 2009 · Verified 6 Jul 2026.
Options
- A
f is one-one but not onto R
- B
f is onto R but not one-one
- C
f is one-one and onto R
- D
f is neither one-one nor onto R
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