If f(x)=x+sinx ,g(x)=e^(-x),u=sqrt(c+1)-...

If `f(x)=x+sinx ,g(x)=e^(-x),u=sqrt(c+1)-sqrt(c)` `v=sqrt(c)` `-sqrt(c-1),(c >1),` then `fog(u)gof(v)` (d) `fog(u)

A

`fog(u)ltfog(v)`

B

`gof(u)ltgof(v)`

C

`gof(u)gtgof(v)`

D

`fog(u)ltfog(v)`

Text Solution

Verified by Experts

The correct Answer is:

4

`u=sqrt(c+1)-sqrt(C )`
`u=(1)/(sqrt(c+1+sqrt(c )) and V-(1)/(sqrt(c-1+sqrt(c ))`
clearly `u lt v`
Also f is increasing whereas g is decreasing Thus
`ultv`
Also f is increasing whereas g is decreasing .Thus
`ultv`
`f(u)lt f(v)`
`gof(u)gtgof(v)`

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