Consider the inequality `9^(x)-a*3^(x)-a+3le0`, where a is a real parameter.
The given inequality has at least one positive solution for `ain`

Options

A. `(-oo,3)`
B. `[2,oo)`
C. `(3,oo)`
D. `[-2,oo)`

Answer

2

Explanation

Given that `9^(x) - a3^(x) - a+3 le 0`
Let `t = 3^(x)`. Then,
`t^(2) -at - a + 3 le 0`
or `t^(3) + 3 le a(t+1) " "(1)`
where `t in R^(+), AA x in R`
Let `f_(1)(t) = t^(2) + 3` and
`f_(2)(t) = a(t+1)`.
In this case both graphs should meet at least once is `t in (0,oo)`. For a= 2 both the curves touch , hence the required range is `a in[2,oo)`