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:
- $\lambda= 0.5$
- $0 < a \leq 2, b > 0$
- $a/\lambda > 2, 0 < b ≤ 1 − \lambda$
Which of the following statements is TRUE?
- The above inequality holds under conditions $(1)$ and $(2)$ but not under condition $(3)$.
- The above inequality holds under conditions $(2)$ and $(3)$ but not under condition $(1)$.
- The above inequality holds under conditions $(1)$ and $(3)$ but not under condition $(2)$.
- The above inequality holds under all the three conditions.
- The above inequality holds under none of the three conditions.