Applications Of Derivatives Question 80
Question: Let $ f’(x)<0 $ and $ g’(x)>0 $ for all real x, then
Options:
A) $ f(g(x+1))>f(g(x+5)) $
B) $ f(g(x)) < f(g(f(x + 2))) $
C) $ g(f(x))<g(f(x+2)) $
D) $ g(f(x))>g(f(x-2)) $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Given, $ f’(x)<0 $ and $ g’(x)>0 $ therefore g(x) is an increasing function and f-(x) is a decreasing function
$ \therefore x+1<x+5\Rightarrow g(x+1)<g(x+5) $
$ \Rightarrow f(g(x+1))>f(g(x+5)) $ Again $ x<x+1\Rightarrow g(x+1)<g(x+5)\Rightarrow f(g(x+1))>f(g(x+5)) $
$ >f(g(x+1)) $
$ x<x+2\Rightarrow f(x)<f(x+2)\Rightarrow g(f(x)) $
$ >g(f(x+1)) $
$ x>x-2\Rightarrow f(x)<f(x-2)\Rightarrow g(f(x)) $
$ <g(f(x-2)) $
BETA
