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If f(x)=-x^(3)-3x^(2)-2x+a,a in R then t...

If f(x)=`-x^(3)-3x^(2)-2x+a,a in R` then the real values of x satisfying `f(x^(2)+1)gtf(2x^(2)+2x+3)` will be

A

`(-oo,oo)`

B

`(0,oo)`

C

`-(oo,0)`

D

`phi`

Text Solution

Verified by Experts

The correct Answer is:
1
f(x)=`-3x^(2)=6x-2lt0 forall x gt 0`
So .,f(X) is decreasing for `x gtx`
Now `x^(2)+1,2x^(2)+2x+3gt0`
`therefore f(x^(2)+1)gtf(2x^(2)+2x+3)`
`rarr x^(2)+1lt2x^(2)+3`
`rarrx^(2)+2x +2 gt0`
`rarr x in R`
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