Let f and g be two differentiable functions on R such that f^ (x)>0 and g^ (x) < 0 for all x ∈ R . Then for all x :

Correct answer: B. f(g(x))>f(g(x+1)) Since f^ (x)>0 and g^ (x) f(x) and g(x+1) < g(x) g[f(x+1)] < g[f(x)] and f[g(x+ 1) ] < f[g(x)] Hence option (b) is correct.

JEE Main 201412 AprilOnline

Exam: JEE Main
Year: 2014
Date: 12 April
Mode: Online
Subject: Mathematics
Chapter: Differentiation

JEE Main 2014 · 12 April · Online · Mathematics · Differentiation

Let f and g be two differentiable functions on R such that f^ (x)>0...

Let

f

and

g

be two differentiable functions on

R

such that

f^{\prime}(x)>0

and

g^{\prime}(x) < 0

for all

x \in R

. Then for all

\mathrm{x}

Options

A $f(g(x))>f(g(x-1))$
B $f(g(x))>f(g(x+1))$
C $g(f(x))>g(f(x-1))$
D $g(f(x)) < g(f(x+1))$

Correct answer

B. $f(g(x))>f(g(x+1))$

Step-by-step solution

Since

f^{\prime}(x)>0

and

g^{\prime}(x) < 0

, therefore

f(x)

is increasing function and

g(x)

is decreasing function.

\Rightarrow f(x+1)>f(x)

and

g(x+1) < g(x)

\Rightarrow g[f(x+1)] < g[f(x)]

and

f[g(x+

] < f[g(x)]

Hence option (b) is correct.

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