If $x ϵ R$ , the solution set of the equation
$4^{- x + 0.5} - {7.2}^{- x} - 4 < 0$ is equal to

(2, \frac{7}{2})

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(- 2, \infty)

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(2, \infty)

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(- \infty, \infty)

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Solution

The correct option is B $(- 2, \infty)$
Put $2^{- x} = t$ and $4^{0.5} = 4^{\frac{1}{2}} = 2$
$∴ 2 t^{2} - 7 t - 4 < 0 \Rightarrow (t - 4) (2 t + 1) < 0$
$- \frac{1}{2} < t < 4 \Rightarrow 0 < 2^{- x} < 2^{2}$
or ${(\frac{1}{2})}^{\infty} < {(\frac{1}{2})}^{x} < {(\frac{1}{2})}^{- 2}$
Since $\frac{1}{2} < 1 ∴ - 2 < x < \infty$
$∴ x ϵ (- 2, \infty) \Rightarrow (b)$

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If xϵR, the solution set of the equation 4−x+0.5−7.2−x−4<0 is equal to

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If $x ϵ R$ , the solution set of the equation
$4^{- x + 0.5} - {7.2}^{- x} - 4 < 0$ is equal to