Question

Let g'(x) > 0 and f’ (x) < 0 ∀ x ∈ R then

• A. g(f(x + 1)) > g(f(x − 1))
• B. f(g(x – 1)) > f(g(x + 1)
• C. g(f(x + 1)) < g(f(x − 1))
• D. g(g(x + 1)) < g(g(x – 1))

Answer 1

Answer: (C)

g(f(x + 1)) < g(f(x − 1))

Answer 2

Clearly g(x) is increasing and f(x) is decreasing ∀ x ∈ R .

⇒ f(x + 1) < f(x - 1) and g(x + 1) > g(x - 1)

⇒ g(f(x + 1)) < g(f(x - 1)).