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Let f'(x) gt0 and g'(x) lt 0 " for all "...

Let `f'(x) gt0 and g'(x) lt 0 " for all " x in R ` Then

A

`f{g(x)gtf(g(X+1)}`

B

`f{g(x)gtf(g(X-1)}`

C

`g{f(x)gtg(f(X+1)}`

D

`g{f(x)gtg(f(X-1)}`

Text Solution

Verified by Experts

The correct Answer is:
A, C
We have `f'(x) gt0 and g'(x) lt 0 " for all " x in R `
`rArr` f(x) is increasing function and g(x) is a decreasing function on R
`rArr f(x-1)ltf(x) ltf(x+1) and g(x-1)gtg(X) gtg(x+1) " for all " x in R`
`rArr g{f(x-1)}gtg{f(x)} gtg{f(x+1)} and , f{g(x)}gtf{g(x)}gtf{g(x+1)} " for all " x in R`
`rArr g{f(x)}gtg{f(x+1)} and f{g(x)} gtf{g(x+1)} " for all " x in R` Hence , optuion (a) and (b) are correct
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