"The domain of the function $$f(x)=\sin ^{-1}\left[2 x^{2}-3\right]+\log _{2}\left(\log _{\frac{1}{2}}\left(x^{2}-5 x+5\right)\right)$$, where [t] is the greatest integer function, is :"

Question

Accepted Answer

"

$- 1 \le 2{x^2} - 3 < 2$

or $2 \le 2{x^2} < 5$

or $1 \le {x^2} < {5 \over 2}$

$$x \in \left( { - \sqrt {{5 \over 2}} , - 1} \right] \cup \left[ {1,\sqrt {{5 \over 2}} } \right)$$

${\log _{{1 \over 2}}}({x^2} - 5x + 5) > 0$

$0 < {x^2} - 5x + 5 < 1$

${x^2} - 5x + 5 > 0$ & ${x^2} - 5x + 4 < 0$

$$x \in \left( { - \infty ,{{5 - \sqrt 5 } \over 2}} \right) \cup \left( {{{5 + \sqrt 5 } \over 2},\infty } \right)$$

& $x \in ( - \infty ,1) \cup (4,\infty )$

Taking intersection

$x \in \left( {1,{{5 - \sqrt 5 } \over 2}} \right)$

"

The domain of the function $$f(x)=\sin ^{-1}\left[2 x^{2}-3\right]+\log _{2}\left(\log _{\frac{1}{2}}\left(x^{2}-5 x+5\right)\right)$$, where [t] is the greatest integer function, is :

Solution

About this question

Drill 25 more like these. Every day. Free.

The domain of the function $$f(x)=\sin ^{-1}\left[2 x^{2}-3\right]+\log _{2}\left(\log _{\frac{1}{2}}\left(x^{2}-5 x+5\right)\right)$$, where [t] is the greatest integer function, is :

Solution

About this question

More Inverse Trigonometric Functions questions

Drill 25 more like these. Every day. Free.