117438 Let \([x]\) denote the greatest integer \(\leq x\), where \(x\) \(\in R\). If the domain of the real valued function \(f(x)=\sqrt{\frac{|[x]|-2}{|[x]|-3}}\) is \((-\infty\), a) \(\cup[b, c) \cup[4, \infty), a\lt \) \(b\lt c\), then the value of \(a+b+c\) is

117439 The real valued function
\(f(x)=\frac{\operatorname{cosec}^{-1} x}{\sqrt{x-[x]}}\), where \([x]\) denotes the greatest integer less than or equal to \(x\), is defined for all \(x\) belonging to

117440 If the function are defined as \(f(x)=\sqrt{x}\) and \(g(x)=\sqrt{1-x}\), then what is the common domain of the following functions?
\(\mathbf{f}+\mathbf{g}, \mathbf{f}-\mathbf{g}, \mathbf{f} / \mathbf{g}, \mathbf{g} / \mathbf{f}, \mathbf{g}-\mathbf{f}\), where \((\mathbf{f} \pm \mathbf{g})(\mathbf{x})=\mathbf{f}(\mathbf{x}) \pm\) \(\mathbf{g}(\mathbf{x}),(\mathbf{f} / \mathbf{g})(\mathbf{x})=\frac{\mathbf{f}(\mathbf{x})}{\mathbf{g}(\mathbf{x})}\)

117441 The domain of the function
\(f(x)=\sin ^{-1}\left(\frac{3 x^2+x-1}{(x-1)^2}\right)+\cos ^{-1}\left(\frac{x-1}{x+1}\right)\) is

117438 Let \([x]\) denote the greatest integer \(\leq x\), where \(x\) \(\in R\). If the domain of the real valued function \(f(x)=\sqrt{\frac{|[x]|-2}{|[x]|-3}}\) is \((-\infty\), a) \(\cup[b, c) \cup[4, \infty), a\lt \) \(b\lt c\), then the value of \(a+b+c\) is

117439 The real valued function
\(f(x)=\frac{\operatorname{cosec}^{-1} x}{\sqrt{x-[x]}}\), where \([x]\) denotes the greatest integer less than or equal to \(x\), is defined for all \(x\) belonging to

117440 If the function are defined as \(f(x)=\sqrt{x}\) and \(g(x)=\sqrt{1-x}\), then what is the common domain of the following functions?
\(\mathbf{f}+\mathbf{g}, \mathbf{f}-\mathbf{g}, \mathbf{f} / \mathbf{g}, \mathbf{g} / \mathbf{f}, \mathbf{g}-\mathbf{f}\), where \((\mathbf{f} \pm \mathbf{g})(\mathbf{x})=\mathbf{f}(\mathbf{x}) \pm\) \(\mathbf{g}(\mathbf{x}),(\mathbf{f} / \mathbf{g})(\mathbf{x})=\frac{\mathbf{f}(\mathbf{x})}{\mathbf{g}(\mathbf{x})}\)

117441 The domain of the function
\(f(x)=\sin ^{-1}\left(\frac{3 x^2+x-1}{(x-1)^2}\right)+\cos ^{-1}\left(\frac{x-1}{x+1}\right)\) is

117438 Let \([x]\) denote the greatest integer \(\leq x\), where \(x\) \(\in R\). If the domain of the real valued function \(f(x)=\sqrt{\frac{|[x]|-2}{|[x]|-3}}\) is \((-\infty\), a) \(\cup[b, c) \cup[4, \infty), a\lt \) \(b\lt c\), then the value of \(a+b+c\) is

117439 The real valued function
\(f(x)=\frac{\operatorname{cosec}^{-1} x}{\sqrt{x-[x]}}\), where \([x]\) denotes the greatest integer less than or equal to \(x\), is defined for all \(x\) belonging to

117440 If the function are defined as \(f(x)=\sqrt{x}\) and \(g(x)=\sqrt{1-x}\), then what is the common domain of the following functions?
\(\mathbf{f}+\mathbf{g}, \mathbf{f}-\mathbf{g}, \mathbf{f} / \mathbf{g}, \mathbf{g} / \mathbf{f}, \mathbf{g}-\mathbf{f}\), where \((\mathbf{f} \pm \mathbf{g})(\mathbf{x})=\mathbf{f}(\mathbf{x}) \pm\) \(\mathbf{g}(\mathbf{x}),(\mathbf{f} / \mathbf{g})(\mathbf{x})=\frac{\mathbf{f}(\mathbf{x})}{\mathbf{g}(\mathbf{x})}\)

117441 The domain of the function
\(f(x)=\sin ^{-1}\left(\frac{3 x^2+x-1}{(x-1)^2}\right)+\cos ^{-1}\left(\frac{x-1}{x+1}\right)\) is

117438 Let \([x]\) denote the greatest integer \(\leq x\), where \(x\) \(\in R\). If the domain of the real valued function \(f(x)=\sqrt{\frac{|[x]|-2}{|[x]|-3}}\) is \((-\infty\), a) \(\cup[b, c) \cup[4, \infty), a\lt \) \(b\lt c\), then the value of \(a+b+c\) is

117439 The real valued function
\(f(x)=\frac{\operatorname{cosec}^{-1} x}{\sqrt{x-[x]}}\), where \([x]\) denotes the greatest integer less than or equal to \(x\), is defined for all \(x\) belonging to

117440 If the function are defined as \(f(x)=\sqrt{x}\) and \(g(x)=\sqrt{1-x}\), then what is the common domain of the following functions?
\(\mathbf{f}+\mathbf{g}, \mathbf{f}-\mathbf{g}, \mathbf{f} / \mathbf{g}, \mathbf{g} / \mathbf{f}, \mathbf{g}-\mathbf{f}\), where \((\mathbf{f} \pm \mathbf{g})(\mathbf{x})=\mathbf{f}(\mathbf{x}) \pm\) \(\mathbf{g}(\mathbf{x}),(\mathbf{f} / \mathbf{g})(\mathbf{x})=\frac{\mathbf{f}(\mathbf{x})}{\mathbf{g}(\mathbf{x})}\)

117441 The domain of the function
\(f(x)=\sin ^{-1}\left(\frac{3 x^2+x-1}{(x-1)^2}\right)+\cos ^{-1}\left(\frac{x-1}{x+1}\right)\) is