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📐 Mathematics Domain Hard mathsparsh_qb

Domain — Question 36

— FD001
The domain of the function $\left[ 2tan\left( \pi x \right) \right]^{{log_{\left[ 2tan\left( \pi x \right) \right]}}\left( g\left( x \right)\right)}$, where $g(x)=\left( \frac{x^{2}+2x-3}{4x^{2}-4x-3} \right)$ contain the interval $[n+\frac{1}{4},n+\frac{1}{2})$, where $n$ is an integer. Then $n$ can be equal to (Note: [.] denotes greatest integer function)
Choose the correct answer
A
-2
B
-1
C
0
D
1
Hint
$log_{f(x)}(g(x))$ is defined if $g(x)>0,f(x)>0,f(x)\neq1$
Step-by-Step Solution

$log_{f(x)}(g(x))$ is defined if $g(x)>0,f(x)>0,f(x)\neq1$
So, $tan(\pi x)\geq 1$ and $x\in \left( -\infty,-3 \right)\cup \left( -\frac{1}{2},1 \right)\cup \left( \frac{3}{2},\infty \right)$

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Question Info
SubjectMathematics
TopicDomain
DifficultyHard
Typesingle_correct
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