Value-of-x-satiesfied-y-log-4-x-2-1-4x-2-2x-1-negative-value-is-a-1-lt-x-lt-2-b-2-lt-x-lt-1-c-2-lt-x-lt-2-d-2-lt-x-lt-1-e-x-lt-2-

Question Number 66355 by gunawan last updated on 13/Aug/19

V alue of x satiesfied y = \frac{\log_{4} (x^{2} - 1)}{4 x^{2} + 2 x + 1}

n e g a t i v e v a l u e is \dots

a . - 1 < x < \sqrt{2}

b . - \sqrt{2} < x < 1

c . - \sqrt{2} < x < \sqrt{2}

d . - \sqrt{2} < x < - 1

e . x < - 2

Commented by kaivan.ahmadi last updated on 13/Aug/19

x^{2} - 1 > 0 \Rightarrow x > 1 o r x < - 1

4 x^{2} + 2 x + 1 > 0 \Rightarrow x \in R

\Rightarrow D_{y} = x > 1 o r x < 0

y < 0 \Rightarrow {l o g}_{4} (x^{2} - 1) < 0 \Rightarrow x^{2} - 1 < 1 \Rightarrow x^{2} < 2 \Rightarrow - \sqrt{2} < x < \sqrt{2}

s o t h e a n s w e r i s - \sqrt{2} < x < - 1 a n d 1 < x < \sqrt{2}