117266
If \(f(x)=\frac{x+1}{x-1}\), then the value of \(f(f(x))\) is equal to
1 \(x\)
2 0
3 \(-x\)
4 1
5 2
Explanation:
A Given, \(f(x)=\frac{x+1}{x-1}\) So, \(f(f(x))=\frac{f(x)+1}{f(x)-1}\) \(=\frac{\frac{x+1}{x-1}+1}{\frac{x+1}{x-1}-1}=\frac{\frac{x+1+x-1}{x-1}}{\frac{x+1-x+1}{x-1}}=\frac{\frac{2 x}{x-1}}{\frac{2}{x-1}}\)Hence, \(\mathrm{f}(\mathrm{f}(\mathrm{x}))=\mathrm{x}\)
Kerala CEE-2017
Sets, Relation and Function
117270
If \(f(x)=x+1\) and \(g(x)=2 x\), the \(f\{g(x)\}\) is equal to
1 \(2(x+1)\)
2 \(2 x(x+1)\)
3 \(\mathrm{x}\)
4 \(2 x+1\)
5 \(2 x^2+1\)
Explanation:
D Given, \(f(x)=x+1\) and \(g(x)=2 x\) \(\therefore \mathrm{f}\{\mathrm{g}(\mathrm{x})\}=\mathrm{f}(2 \mathrm{x})\)Hence, \(\quad=2 \mathrm{x}+1\)
Kerala CEE-2012
Sets, Relation and Function
117251
If the relation \(R: A \rightarrow B\), where \(A=\) \(\{1,2,3,4\}\) and \(B=\{1,3,5\}\) is defined by \(R=\) \(\{(x, y): x\lt y, x \in A, y \in B\}\), then \(R^{-1} O R\) is equal to
1 \(\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}\)
2 \(\{(3,1),(5,1),(5,2),(5,3),(5,4)\}\)
3 \(\{(3,3),(3,5),(5,3),(5,5)\}\)
4 None of the above
Explanation:
C \(\mathrm{R}=\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}\) \(\mathrm{R}^{-1}=\{(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)\}\)Thus, \(\mathrm{R}^{-1} \mathrm{OR}=\{(3,5),(5,5),(3,3),(5,3)\}\)
117266
If \(f(x)=\frac{x+1}{x-1}\), then the value of \(f(f(x))\) is equal to
1 \(x\)
2 0
3 \(-x\)
4 1
5 2
Explanation:
A Given, \(f(x)=\frac{x+1}{x-1}\) So, \(f(f(x))=\frac{f(x)+1}{f(x)-1}\) \(=\frac{\frac{x+1}{x-1}+1}{\frac{x+1}{x-1}-1}=\frac{\frac{x+1+x-1}{x-1}}{\frac{x+1-x+1}{x-1}}=\frac{\frac{2 x}{x-1}}{\frac{2}{x-1}}\)Hence, \(\mathrm{f}(\mathrm{f}(\mathrm{x}))=\mathrm{x}\)
Kerala CEE-2017
Sets, Relation and Function
117270
If \(f(x)=x+1\) and \(g(x)=2 x\), the \(f\{g(x)\}\) is equal to
1 \(2(x+1)\)
2 \(2 x(x+1)\)
3 \(\mathrm{x}\)
4 \(2 x+1\)
5 \(2 x^2+1\)
Explanation:
D Given, \(f(x)=x+1\) and \(g(x)=2 x\) \(\therefore \mathrm{f}\{\mathrm{g}(\mathrm{x})\}=\mathrm{f}(2 \mathrm{x})\)Hence, \(\quad=2 \mathrm{x}+1\)
Kerala CEE-2012
Sets, Relation and Function
117251
If the relation \(R: A \rightarrow B\), where \(A=\) \(\{1,2,3,4\}\) and \(B=\{1,3,5\}\) is defined by \(R=\) \(\{(x, y): x\lt y, x \in A, y \in B\}\), then \(R^{-1} O R\) is equal to
1 \(\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}\)
2 \(\{(3,1),(5,1),(5,2),(5,3),(5,4)\}\)
3 \(\{(3,3),(3,5),(5,3),(5,5)\}\)
4 None of the above
Explanation:
C \(\mathrm{R}=\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}\) \(\mathrm{R}^{-1}=\{(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)\}\)Thus, \(\mathrm{R}^{-1} \mathrm{OR}=\{(3,5),(5,5),(3,3),(5,3)\}\)
117266
If \(f(x)=\frac{x+1}{x-1}\), then the value of \(f(f(x))\) is equal to
1 \(x\)
2 0
3 \(-x\)
4 1
5 2
Explanation:
A Given, \(f(x)=\frac{x+1}{x-1}\) So, \(f(f(x))=\frac{f(x)+1}{f(x)-1}\) \(=\frac{\frac{x+1}{x-1}+1}{\frac{x+1}{x-1}-1}=\frac{\frac{x+1+x-1}{x-1}}{\frac{x+1-x+1}{x-1}}=\frac{\frac{2 x}{x-1}}{\frac{2}{x-1}}\)Hence, \(\mathrm{f}(\mathrm{f}(\mathrm{x}))=\mathrm{x}\)
Kerala CEE-2017
Sets, Relation and Function
117270
If \(f(x)=x+1\) and \(g(x)=2 x\), the \(f\{g(x)\}\) is equal to
1 \(2(x+1)\)
2 \(2 x(x+1)\)
3 \(\mathrm{x}\)
4 \(2 x+1\)
5 \(2 x^2+1\)
Explanation:
D Given, \(f(x)=x+1\) and \(g(x)=2 x\) \(\therefore \mathrm{f}\{\mathrm{g}(\mathrm{x})\}=\mathrm{f}(2 \mathrm{x})\)Hence, \(\quad=2 \mathrm{x}+1\)
Kerala CEE-2012
Sets, Relation and Function
117251
If the relation \(R: A \rightarrow B\), where \(A=\) \(\{1,2,3,4\}\) and \(B=\{1,3,5\}\) is defined by \(R=\) \(\{(x, y): x\lt y, x \in A, y \in B\}\), then \(R^{-1} O R\) is equal to
1 \(\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}\)
2 \(\{(3,1),(5,1),(5,2),(5,3),(5,4)\}\)
3 \(\{(3,3),(3,5),(5,3),(5,5)\}\)
4 None of the above
Explanation:
C \(\mathrm{R}=\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}\) \(\mathrm{R}^{-1}=\{(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)\}\)Thus, \(\mathrm{R}^{-1} \mathrm{OR}=\{(3,5),(5,5),(3,3),(5,3)\}\)
117266
If \(f(x)=\frac{x+1}{x-1}\), then the value of \(f(f(x))\) is equal to
1 \(x\)
2 0
3 \(-x\)
4 1
5 2
Explanation:
A Given, \(f(x)=\frac{x+1}{x-1}\) So, \(f(f(x))=\frac{f(x)+1}{f(x)-1}\) \(=\frac{\frac{x+1}{x-1}+1}{\frac{x+1}{x-1}-1}=\frac{\frac{x+1+x-1}{x-1}}{\frac{x+1-x+1}{x-1}}=\frac{\frac{2 x}{x-1}}{\frac{2}{x-1}}\)Hence, \(\mathrm{f}(\mathrm{f}(\mathrm{x}))=\mathrm{x}\)
Kerala CEE-2017
Sets, Relation and Function
117270
If \(f(x)=x+1\) and \(g(x)=2 x\), the \(f\{g(x)\}\) is equal to
1 \(2(x+1)\)
2 \(2 x(x+1)\)
3 \(\mathrm{x}\)
4 \(2 x+1\)
5 \(2 x^2+1\)
Explanation:
D Given, \(f(x)=x+1\) and \(g(x)=2 x\) \(\therefore \mathrm{f}\{\mathrm{g}(\mathrm{x})\}=\mathrm{f}(2 \mathrm{x})\)Hence, \(\quad=2 \mathrm{x}+1\)
Kerala CEE-2012
Sets, Relation and Function
117251
If the relation \(R: A \rightarrow B\), where \(A=\) \(\{1,2,3,4\}\) and \(B=\{1,3,5\}\) is defined by \(R=\) \(\{(x, y): x\lt y, x \in A, y \in B\}\), then \(R^{-1} O R\) is equal to
1 \(\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}\)
2 \(\{(3,1),(5,1),(5,2),(5,3),(5,4)\}\)
3 \(\{(3,3),(3,5),(5,3),(5,5)\}\)
4 None of the above
Explanation:
C \(\mathrm{R}=\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}\) \(\mathrm{R}^{-1}=\{(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)\}\)Thus, \(\mathrm{R}^{-1} \mathrm{OR}=\{(3,5),(5,5),(3,3),(5,3)\}\)
117266
If \(f(x)=\frac{x+1}{x-1}\), then the value of \(f(f(x))\) is equal to
1 \(x\)
2 0
3 \(-x\)
4 1
5 2
Explanation:
A Given, \(f(x)=\frac{x+1}{x-1}\) So, \(f(f(x))=\frac{f(x)+1}{f(x)-1}\) \(=\frac{\frac{x+1}{x-1}+1}{\frac{x+1}{x-1}-1}=\frac{\frac{x+1+x-1}{x-1}}{\frac{x+1-x+1}{x-1}}=\frac{\frac{2 x}{x-1}}{\frac{2}{x-1}}\)Hence, \(\mathrm{f}(\mathrm{f}(\mathrm{x}))=\mathrm{x}\)
Kerala CEE-2017
Sets, Relation and Function
117270
If \(f(x)=x+1\) and \(g(x)=2 x\), the \(f\{g(x)\}\) is equal to
1 \(2(x+1)\)
2 \(2 x(x+1)\)
3 \(\mathrm{x}\)
4 \(2 x+1\)
5 \(2 x^2+1\)
Explanation:
D Given, \(f(x)=x+1\) and \(g(x)=2 x\) \(\therefore \mathrm{f}\{\mathrm{g}(\mathrm{x})\}=\mathrm{f}(2 \mathrm{x})\)Hence, \(\quad=2 \mathrm{x}+1\)
Kerala CEE-2012
Sets, Relation and Function
117251
If the relation \(R: A \rightarrow B\), where \(A=\) \(\{1,2,3,4\}\) and \(B=\{1,3,5\}\) is defined by \(R=\) \(\{(x, y): x\lt y, x \in A, y \in B\}\), then \(R^{-1} O R\) is equal to
1 \(\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}\)
2 \(\{(3,1),(5,1),(5,2),(5,3),(5,4)\}\)
3 \(\{(3,3),(3,5),(5,3),(5,5)\}\)
4 None of the above
Explanation:
C \(\mathrm{R}=\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}\) \(\mathrm{R}^{-1}=\{(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)\}\)Thus, \(\mathrm{R}^{-1} \mathrm{OR}=\{(3,5),(5,5),(3,3),(5,3)\}\)