Question

The solution of the inequation 4^{–x + 0.5} – 7.2^–x< 4, x ∈ R, is :

• A. (–2, ∞)
• B. (2, ∞)
• C. $\left( 2,\frac{7}{2} \right)$
• D. None of these

Answer 1

Answer: (A)

(–2, ∞)

Answer 2

Let 2^–x = t   ∴ t > 0 . . . (i)

∴ 2t² – 7t < 4

⇒ $\frac{–1}{2}$ < t < 4 . . . (ii)

from (i) & (ii)

0 < t < 4

0 < 2^–x < 4

⇒ –2 < x < ∞ 

⇒ x ∈ (–2, ∞)