A) \[\left( -2,\infty \right)\]
B) \[\left( 2,6 \right)\]
C) \[\left( 2,\frac{7}{2} \right)\]
D) \[\left( 2,14 \right)\]
Correct Answer: A
Solution :
(a): The given in equation is \[{{4}^{-x+0.5}}-{{7.2}^{-x}}<4,x\in R\] Let \[{{2}^{-x}}=t\,\,\,\therefore \,\,\,2{{t}^{2}}-7t<4\Rightarrow 2{{t}^{2}}-7t-4<0\] \[\Rightarrow \left( 2t+1 \right)\left( t-4 \right)<0\Rightarrow \frac{-1}{2}<t<4\] But, \[{{2}^{-x}}>0\] So, \[0<t<4\Rightarrow 0<{{2}^{-x}}<4\Rightarrow -2<x<\infty \] Or \[x\in \left( -2,\infty \right)\]
You need to login to perform this action.
You will be redirected in
3 sec
