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JEE Main2014MathematicsDifferentiationActual

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 :

Options

  1. Af(g(x))>f(g(x-1))
  2. Bf(g(x))>f(g(x+1))
  3. Cg(f(x))>g(f(x-1))
  4. Dg(f(x)) < g(f(x+1))

Correct answer

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

Step-by-step solution

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.

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