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Let f(x) be a non-positive continuous fu...

Let `f(x)` be a non-positive continuous function and `F(x)=int_(0)^(x)f(t)dt AA x ge0` and `f(x) ge cF(x)` where `c lt 0` and let `g:[0, infty) to R` be a function such that `(dg(x))/(dx) lt g(x) AA x gt 0` and `g(0)=0`
The solution set of inequation `g(x)(cos^(-1)x-sin^(-1)) le0`

A

`[-1,1/sqrt(2)]`

B

`[1/sqrt(2),1]`

C

`[0,1/sqrt(2)]`

D

`[0,1/sqrt(2)]`

Text Solution

Verified by Experts

The correct Answer is:
A
`g(x) (cos^(-1)x-sin^(-1)x) le0`
or `(cos^(-1)x-sin^(-1)x) ge0` or `x in [-1, 1/sqrt(2)]`
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