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

(0,2)

B

(-2,2)

C

`(-2,1) cup(1, oo)`

D

`(-oo , -2)cup (0,2)`

Text Solution

Verified by Experts

The correct Answer is:

D

We have `f(x)=1-x-x^3`
`therefore f(x) =-1 -3x^2 lt 0 " for all " x in R `
`rArr f(x)=-1-3x^2 lt 0 for all x in R `
Now `1- f(x)=f^3(x) gt f(1-5x)`
`rArr f(f(x)) gt f(1-5x)`
`f(x) gt 1-5x`
`rArr 1-x-x^3 gt 1-5x`
`rArr x^3-4x lt 0`
`rArr x(x-2)(x+2) lt 0 `
`rArr x in (-oo,-2)cup (0,2)`

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