Domain, Co-domain and Range of Function
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Sets, Relation and Function

117423 If the range of the function \(f(x)=-3 x-3\) is \(\{3\), \(-6,-9,-18\}\), then which of the following elements is not in the domain of \(f\) ?

1 -1
2 -2
3 1
4 2
TS EAMCET-2017
Sets, Relation and Function

117424 \(f:(-\infty, 0] \rightarrow[0, \infty)\) is defind as \(f(x)=x^2\). The domain and range of its inverse is

1 Domain \(\left(\mathrm{f}^{-1}\right)=[0, \infty)\), Range of \(\left(\mathrm{f}^{-1}\right)=(-\infty\), \(0]\)
2 Domain of \(\left(\mathrm{f}^{-1}\right)=[0, \infty)\) Range of \(\left(\mathrm{f}^{-1}\right)=(-\infty\), \(\infty)\)
3 Domain of \(\left(f^{-1}\right)=[0, \infty)\) Range of \(\left(f^{-1}\right)=(0\), \(\infty)\)
4 \(\mathrm{f}^{-1}\) does not exist
TS EAMCET-2017
Sets, Relation and Function

117425 Let the sets \(A\) and \(B\) denote the domain and range respectively of the function
\(f(x)=\frac{1}{\sqrt{[x]-x}}\) where \([x]\) denotes the smallest integer greater than or equal to \(x\). Then among the statements
\(\left(S_1\right): A \cap B=(1, \infty)-N\) and
\(\left(S_2\right): A \cup B=(1, \infty)\)

1 only \(\left(\mathrm{S}_1\right)\) is true
2 both \(\left(\mathrm{S}_1\right)\) and \(\left(\mathrm{S}_2\right)\) are true
3 neither \(\left(\mathrm{S}_1\right)\) nor \(\left(\mathrm{S}_2\right)\) is true
4 only \(\left(\mathrm{S}_2\right)\) is true
JEE Main-06.04.2023
Sets, Relation and Function

117426 The domain of the function \(f(x)=\sin ^{-1}\left(\frac{x^2-3 x+2}{x^2+2 x+7}\right)\) is

1 \([1, \infty]\)
2 \((-1,2]\)
3 \([-1, \infty]\)
4 \([-\infty, 2]\)
JEE Main-29.07.2022
Sets, Relation and Function

117427 If \(f(x)=3-x,-4 \leq x \leq 4\), then the domain of \(\log _e\) (f(x)) is

1 \([-4,4]\)
2 \((-\infty, 3]\)
3 \((-\infty, 3)\)
4 \([-4,3)\)
J and K CET-2011
Join With Us for More Updates
Sets, Relation and Function

117423 If the range of the function \(f(x)=-3 x-3\) is \(\{3\), \(-6,-9,-18\}\), then which of the following elements is not in the domain of \(f\) ?

1 -1
2 -2
3 1
4 2
TS EAMCET-2017
Sets, Relation and Function

117424 \(f:(-\infty, 0] \rightarrow[0, \infty)\) is defind as \(f(x)=x^2\). The domain and range of its inverse is

1 Domain \(\left(\mathrm{f}^{-1}\right)=[0, \infty)\), Range of \(\left(\mathrm{f}^{-1}\right)=(-\infty\), \(0]\)
2 Domain of \(\left(\mathrm{f}^{-1}\right)=[0, \infty)\) Range of \(\left(\mathrm{f}^{-1}\right)=(-\infty\), \(\infty)\)
3 Domain of \(\left(f^{-1}\right)=[0, \infty)\) Range of \(\left(f^{-1}\right)=(0\), \(\infty)\)
4 \(\mathrm{f}^{-1}\) does not exist
TS EAMCET-2017
Sets, Relation and Function

117425 Let the sets \(A\) and \(B\) denote the domain and range respectively of the function
\(f(x)=\frac{1}{\sqrt{[x]-x}}\) where \([x]\) denotes the smallest integer greater than or equal to \(x\). Then among the statements
\(\left(S_1\right): A \cap B=(1, \infty)-N\) and
\(\left(S_2\right): A \cup B=(1, \infty)\)

1 only \(\left(\mathrm{S}_1\right)\) is true
2 both \(\left(\mathrm{S}_1\right)\) and \(\left(\mathrm{S}_2\right)\) are true
3 neither \(\left(\mathrm{S}_1\right)\) nor \(\left(\mathrm{S}_2\right)\) is true
4 only \(\left(\mathrm{S}_2\right)\) is true
JEE Main-06.04.2023
Sets, Relation and Function

117426 The domain of the function \(f(x)=\sin ^{-1}\left(\frac{x^2-3 x+2}{x^2+2 x+7}\right)\) is

1 \([1, \infty]\)
2 \((-1,2]\)
3 \([-1, \infty]\)
4 \([-\infty, 2]\)
JEE Main-29.07.2022
Sets, Relation and Function

117427 If \(f(x)=3-x,-4 \leq x \leq 4\), then the domain of \(\log _e\) (f(x)) is

1 \([-4,4]\)
2 \((-\infty, 3]\)
3 \((-\infty, 3)\)
4 \([-4,3)\)
J and K CET-2011
For More Updates join with Us
Sets, Relation and Function

117423 If the range of the function \(f(x)=-3 x-3\) is \(\{3\), \(-6,-9,-18\}\), then which of the following elements is not in the domain of \(f\) ?

1 -1
2 -2
3 1
4 2
TS EAMCET-2017
Sets, Relation and Function

117424 \(f:(-\infty, 0] \rightarrow[0, \infty)\) is defind as \(f(x)=x^2\). The domain and range of its inverse is

1 Domain \(\left(\mathrm{f}^{-1}\right)=[0, \infty)\), Range of \(\left(\mathrm{f}^{-1}\right)=(-\infty\), \(0]\)
2 Domain of \(\left(\mathrm{f}^{-1}\right)=[0, \infty)\) Range of \(\left(\mathrm{f}^{-1}\right)=(-\infty\), \(\infty)\)
3 Domain of \(\left(f^{-1}\right)=[0, \infty)\) Range of \(\left(f^{-1}\right)=(0\), \(\infty)\)
4 \(\mathrm{f}^{-1}\) does not exist
TS EAMCET-2017
Sets, Relation and Function

117425 Let the sets \(A\) and \(B\) denote the domain and range respectively of the function
\(f(x)=\frac{1}{\sqrt{[x]-x}}\) where \([x]\) denotes the smallest integer greater than or equal to \(x\). Then among the statements
\(\left(S_1\right): A \cap B=(1, \infty)-N\) and
\(\left(S_2\right): A \cup B=(1, \infty)\)

1 only \(\left(\mathrm{S}_1\right)\) is true
2 both \(\left(\mathrm{S}_1\right)\) and \(\left(\mathrm{S}_2\right)\) are true
3 neither \(\left(\mathrm{S}_1\right)\) nor \(\left(\mathrm{S}_2\right)\) is true
4 only \(\left(\mathrm{S}_2\right)\) is true
JEE Main-06.04.2023
Sets, Relation and Function

117426 The domain of the function \(f(x)=\sin ^{-1}\left(\frac{x^2-3 x+2}{x^2+2 x+7}\right)\) is

1 \([1, \infty]\)
2 \((-1,2]\)
3 \([-1, \infty]\)
4 \([-\infty, 2]\)
JEE Main-29.07.2022
Sets, Relation and Function

117427 If \(f(x)=3-x,-4 \leq x \leq 4\), then the domain of \(\log _e\) (f(x)) is

1 \([-4,4]\)
2 \((-\infty, 3]\)
3 \((-\infty, 3)\)
4 \([-4,3)\)
J and K CET-2011
NEET DIGITAL LIBRARY
Sets, Relation and Function

117423 If the range of the function \(f(x)=-3 x-3\) is \(\{3\), \(-6,-9,-18\}\), then which of the following elements is not in the domain of \(f\) ?

1 -1
2 -2
3 1
4 2
TS EAMCET-2017
Sets, Relation and Function

117424 \(f:(-\infty, 0] \rightarrow[0, \infty)\) is defind as \(f(x)=x^2\). The domain and range of its inverse is

1 Domain \(\left(\mathrm{f}^{-1}\right)=[0, \infty)\), Range of \(\left(\mathrm{f}^{-1}\right)=(-\infty\), \(0]\)
2 Domain of \(\left(\mathrm{f}^{-1}\right)=[0, \infty)\) Range of \(\left(\mathrm{f}^{-1}\right)=(-\infty\), \(\infty)\)
3 Domain of \(\left(f^{-1}\right)=[0, \infty)\) Range of \(\left(f^{-1}\right)=(0\), \(\infty)\)
4 \(\mathrm{f}^{-1}\) does not exist
TS EAMCET-2017
Sets, Relation and Function

117425 Let the sets \(A\) and \(B\) denote the domain and range respectively of the function
\(f(x)=\frac{1}{\sqrt{[x]-x}}\) where \([x]\) denotes the smallest integer greater than or equal to \(x\). Then among the statements
\(\left(S_1\right): A \cap B=(1, \infty)-N\) and
\(\left(S_2\right): A \cup B=(1, \infty)\)

1 only \(\left(\mathrm{S}_1\right)\) is true
2 both \(\left(\mathrm{S}_1\right)\) and \(\left(\mathrm{S}_2\right)\) are true
3 neither \(\left(\mathrm{S}_1\right)\) nor \(\left(\mathrm{S}_2\right)\) is true
4 only \(\left(\mathrm{S}_2\right)\) is true
JEE Main-06.04.2023
Sets, Relation and Function

117426 The domain of the function \(f(x)=\sin ^{-1}\left(\frac{x^2-3 x+2}{x^2+2 x+7}\right)\) is

1 \([1, \infty]\)
2 \((-1,2]\)
3 \([-1, \infty]\)
4 \([-\infty, 2]\)
JEE Main-29.07.2022
Sets, Relation and Function

117427 If \(f(x)=3-x,-4 \leq x \leq 4\), then the domain of \(\log _e\) (f(x)) is

1 \([-4,4]\)
2 \((-\infty, 3]\)
3 \((-\infty, 3)\)
4 \([-4,3)\)
J and K CET-2011
Join With Us for More Updates
Sets, Relation and Function

117423 If the range of the function \(f(x)=-3 x-3\) is \(\{3\), \(-6,-9,-18\}\), then which of the following elements is not in the domain of \(f\) ?

1 -1
2 -2
3 1
4 2
TS EAMCET-2017
Sets, Relation and Function

117424 \(f:(-\infty, 0] \rightarrow[0, \infty)\) is defind as \(f(x)=x^2\). The domain and range of its inverse is

1 Domain \(\left(\mathrm{f}^{-1}\right)=[0, \infty)\), Range of \(\left(\mathrm{f}^{-1}\right)=(-\infty\), \(0]\)
2 Domain of \(\left(\mathrm{f}^{-1}\right)=[0, \infty)\) Range of \(\left(\mathrm{f}^{-1}\right)=(-\infty\), \(\infty)\)
3 Domain of \(\left(f^{-1}\right)=[0, \infty)\) Range of \(\left(f^{-1}\right)=(0\), \(\infty)\)
4 \(\mathrm{f}^{-1}\) does not exist
TS EAMCET-2017
Sets, Relation and Function

117425 Let the sets \(A\) and \(B\) denote the domain and range respectively of the function
\(f(x)=\frac{1}{\sqrt{[x]-x}}\) where \([x]\) denotes the smallest integer greater than or equal to \(x\). Then among the statements
\(\left(S_1\right): A \cap B=(1, \infty)-N\) and
\(\left(S_2\right): A \cup B=(1, \infty)\)

1 only \(\left(\mathrm{S}_1\right)\) is true
2 both \(\left(\mathrm{S}_1\right)\) and \(\left(\mathrm{S}_2\right)\) are true
3 neither \(\left(\mathrm{S}_1\right)\) nor \(\left(\mathrm{S}_2\right)\) is true
4 only \(\left(\mathrm{S}_2\right)\) is true
JEE Main-06.04.2023
Sets, Relation and Function

117426 The domain of the function \(f(x)=\sin ^{-1}\left(\frac{x^2-3 x+2}{x^2+2 x+7}\right)\) is

1 \([1, \infty]\)
2 \((-1,2]\)
3 \([-1, \infty]\)
4 \([-\infty, 2]\)
JEE Main-29.07.2022
Sets, Relation and Function

117427 If \(f(x)=3-x,-4 \leq x \leq 4\), then the domain of \(\log _e\) (f(x)) is

1 \([-4,4]\)
2 \((-\infty, 3]\)
3 \((-\infty, 3)\)
4 \([-4,3)\)
J and K CET-2011