Question

Let g ' (x) > 0 and f ' (x) < 0 " x Ī R then

• A. g(f(x + 1)) > g(f(x – 1))
• B. g(g(x + 1)) < g(g(x – 1))
• C. g(f(x + 1)) < g(f(x – 1))
• D. None of these

Answer 1

Answer: (A)

g(f(x + 1)) > g(f(x – 1))

Answer 2

x + 1 > x – 1

If f is increasing

f(x + 1) > f(x – 1)

g is decreasing g(f(x + 1)) < g(f(x – 1))

x + 1 > x – 1

g is decreasing g(x + 1) < g(x – 1)

f is increasing f(g (x + 1)) < f(g(x – 1))