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Let $f(x)= 2^{x}$. Consider the following inequality for real numbers $a, b$ and $0 < \lambda < 1$:

$f(\lambda a + b) \leq \lambda f(a) + (1 - \lambda) f (\frac{b}{1 - \lambda})$.

Consider the following 3 conditions:

  1. $\lambda= 0.5$
  2. $0 < a \leq 2, b > 0$
  3. $a/\lambda > 2, 0 < b ≤ 1 − \lambda$

Which of the following statements is TRUE?

  1. The above inequality holds under conditions $(1)$ and $(2)$ but not under condition $(3)$.
  2. The above inequality holds under conditions $(2)$ and $(3)$ but not under condition $(1)$.
  3. The above inequality holds under conditions $(1)$ and $(3)$ but not under condition $(2)$.
  4. The above inequality holds under all the three conditions.
  5. The above inequality holds under none of the three conditions.
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