JEE Main2009MathematicsFunctionsActual

For real x , let f(x)=x^3+5 x+1 , then

Options

Af is one-one but not onto R
Bf is onto R but not one-one
Cf is one-one and onto R
Df is neither one-one nor onto R

Correct answer

C. f is one-one and onto R

Step-by-step solution

Given f(x)=x^3+5 x+1 Now f^ (x)=3 x^2+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 , Lt _ x - f(x)=- and Lt _ x f(x)= f ( x ) takes every value between - and . Thus, f(x) is onto function.

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