The-domain-of-f-x-2-2-x-2-2x-is-

Question Number 13811 by Tinkutara last updated on 23/May/17

The domain of f (x) = \sqrt{2 - 2^{x} - 2^{2 x}} is ?

Commented by RasheedSindhi last updated on 24/May/17

Sorry, wrong process .

Answered by ajfour last updated on 23/May/17

l e t 2^{x} = t > 0 \dots . (i)

\Rightarrow t^{2} + t - 2 ⩽ 0

t^{2} + 2 t - t - 2 ⩽ 0

(t - 1) (t + 2) ⩽ 0

\Rightarrow - 2 ⩽ t ⩽ 1 \dots . (i i)

f r o m (i) a n d (i i),

0 < t (= 2^{x}) ⩽ 1

\Rightarrow x \in (- \infty, 0] .

Commented by Tinkutara last updated on 23/May/17

Thanks .