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Let f(x)=1-x-x^(3). Then, the real value...

Let `f(x)=1-x-x^(3)`. Then, the real values of x satisfying the inequality,
`1-f(x)-f^(3)(x) gt f(1-5x)`, are

A

`(-2,0)`

B

`(2,oo)`

C

`(0,2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=1-x-x^(3)`
`rArr" "f'(x)=-1-3x^(2)lt0` for all x
Now `1-f(x)-f^(3)(x)gtf(1-5x)`
`rArr" "f(f(x))gtf(1-5x)`
`rArr" "f(x)lt1-5x" (as f(x) is decreasing)"`
`rArr" "1-x-x^(3)lt1-5x`
`rArr" "x^(3)-4xgt0`
`rArr" "x(x-2)(x+2)gt0`
`rArr" "x in (-2,0)uu(2,oo)`
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