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Question

For real x, let f(x)=x3+5x+1, then


A

f is onto R but not one-one

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B

f is one-one and onto R

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C

f is neither one-one nor onto R

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D

f is one-one but not onto R

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Solution

The correct option is B

f is one-one and onto R


Given that f(x)=x3+5x+1
f(x)=3x2+5>0,xR f(x) is strictly increasing on R f(x) is one-one
Since f(x) is a polynomial function which is continuous and increasing on R
with limxf(x)=
and limxf(x)= Range of f=(,)=R
Hence f is onto also. So, f is one-one and onto R.


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