Question

what is the domain of sqrt(4(8x^2-5)-7)? Please note the answer must be in INTERVAL NOTATION. Thank you.

Answer 1

\[f:f(x)=\sqrt{4(x ^{2}-5)-7}\]
We have to know a little about radication here, what can we NOt do in radication?
and we can observe we don't have any restrictions.
So we can conclude that the domain is all the real numbers.
we write it this way:
D(f)= R

Answer 2

or if you please: \[(-\infty;\infty)\]

Answer 3

\[domain is all real values for which 4\left( x ^{2}-5 \right)-7\ge0\]
\[4\left( x ^{2}-5 \right)\ge 7,x ^{2}-5\ge \frac{ 7 }{ 4 }\]
\[x ^{2}\ge 5+\frac{ 7 }{4 }\]
\[\left| x \right|\ge \frac{ 3\sqrt{3} }{2 }\]
\[x \le \frac{- 3\sqrt{3} }{2 }orx \ge \frac{ 3\sqrt{3} }{ 2 }\]