Solve `4^(-x+0.5)-7.2^(-x)lt 4 `

Options

A. R
B. `(-2,oo)`
C. `(2,oo)`
D. `(2,7//2)`

Answer

B

Explanation

we have,
`4^(-x+0.5)-7(2^(-1))-4 lt 0`
`rArr 4^(-x)xx4^(1//2)-7xx2^(-X)-4 lt 0`
`rArr 2(2^(-x))^(2)-7(2^(-x))-4 lt 0`
`rArr 2(2^(-x))^(2)-8(2^(-x))+2^(-x)-4 lt 0`
`rArr (2^(-x)-4)(2xx2^(-x)+1) lt 0`
`rArr 2^(-x-4) lt 0 " "[:' 2xx2^(-x)+1 gt 0" for all " x in R]`
`rArr 2^(-x) lt 2^(2) implies -x lt 2 rArr x gt-2 rArr x in (-,oo)`