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

117405 \(\frac{x-1}{3 x+4}\lt \frac{x-3}{3 x-2}\) holds, for all \(x\) in the interval

1 \(\left(\frac{-4}{3}, \frac{2}{3}\right)\)
2 \(\left(-\infty, \frac{-5}{4}\right)\)
3 \(\left(\frac{3}{3}, \infty\right)\)
4 \(\left(-\infty, \frac{-5}{4}\right) \cup\left(\frac{3}{4},-\infty\right)\)
AP EAMCET-2017
Sets, Relation and Function

117406 Let \(A=\{-4,-2,-1,0,3,5\}, f: A \rightarrow I R \quad\) be defined by
\(f(x)=\left\{\begin{array}{ccc}\mathbf{3 x}-1 & \text { for } & \mathbf{x}>\mathbf{3} \\ \mathbf{x}^2+1 & \text { for } & -\mathbf{3} \leq \mathbf{x} \leq \mathbf{3} \\ \mathbf{2 x}-\mathbf{3} & \text { for } & \mathbf{x}\lt -\mathbf{3}\end{array}\right.\)
Then the range of \(f\) is

1 \(\{-11,5,2,1,10,14\}\)
2 \(\{-11,-2,2,1,8,14\}\)
3 \(\{-11,5,2,1,8,14\}\)
4 \(\{-11,-7,-5,1,10,14\}\)
AP EAMCET-2017
Sets, Relation and Function

117407 The range of the function \(f(x)=\frac{x}{x^2-5 x+9}\) is

1 \(\left[\frac{1}{11}, 1\right]\)
2 \(\left[\frac{-1}{11}, 1\right]\)
3 \(\left[-1, \frac{-1}{11}\right]\)
4 \(\left[-1, \frac{1}{11}\right]\)
AP EAMCET-08.07.2022
Sets, Relation and Function

117408 The domain of the real valued function \(f(x)=\) \(\sqrt{\frac{\mathbf{2 - | x |}}{\mathbf{3}-|\mathbf{x}|}}\) is

1 \((-\infty, \infty)\)
2 \((-\infty,-3) \cup(2, \infty)\)
3 \((-\infty,-3) \cup(-2,2) \cup[3, \infty)\)
4 \((-\infty,-3) \cup[-2,2] \cup(3, \infty)\)
AP EAMCET-08.07.2022
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Sets, Relation and Function

117405 \(\frac{x-1}{3 x+4}\lt \frac{x-3}{3 x-2}\) holds, for all \(x\) in the interval

1 \(\left(\frac{-4}{3}, \frac{2}{3}\right)\)
2 \(\left(-\infty, \frac{-5}{4}\right)\)
3 \(\left(\frac{3}{3}, \infty\right)\)
4 \(\left(-\infty, \frac{-5}{4}\right) \cup\left(\frac{3}{4},-\infty\right)\)
AP EAMCET-2017
Sets, Relation and Function

117406 Let \(A=\{-4,-2,-1,0,3,5\}, f: A \rightarrow I R \quad\) be defined by
\(f(x)=\left\{\begin{array}{ccc}\mathbf{3 x}-1 & \text { for } & \mathbf{x}>\mathbf{3} \\ \mathbf{x}^2+1 & \text { for } & -\mathbf{3} \leq \mathbf{x} \leq \mathbf{3} \\ \mathbf{2 x}-\mathbf{3} & \text { for } & \mathbf{x}\lt -\mathbf{3}\end{array}\right.\)
Then the range of \(f\) is

1 \(\{-11,5,2,1,10,14\}\)
2 \(\{-11,-2,2,1,8,14\}\)
3 \(\{-11,5,2,1,8,14\}\)
4 \(\{-11,-7,-5,1,10,14\}\)
AP EAMCET-2017
Sets, Relation and Function

117407 The range of the function \(f(x)=\frac{x}{x^2-5 x+9}\) is

1 \(\left[\frac{1}{11}, 1\right]\)
2 \(\left[\frac{-1}{11}, 1\right]\)
3 \(\left[-1, \frac{-1}{11}\right]\)
4 \(\left[-1, \frac{1}{11}\right]\)
AP EAMCET-08.07.2022
Sets, Relation and Function

117408 The domain of the real valued function \(f(x)=\) \(\sqrt{\frac{\mathbf{2 - | x |}}{\mathbf{3}-|\mathbf{x}|}}\) is

1 \((-\infty, \infty)\)
2 \((-\infty,-3) \cup(2, \infty)\)
3 \((-\infty,-3) \cup(-2,2) \cup[3, \infty)\)
4 \((-\infty,-3) \cup[-2,2] \cup(3, \infty)\)
AP EAMCET-08.07.2022
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Sets, Relation and Function

117405 \(\frac{x-1}{3 x+4}\lt \frac{x-3}{3 x-2}\) holds, for all \(x\) in the interval

1 \(\left(\frac{-4}{3}, \frac{2}{3}\right)\)
2 \(\left(-\infty, \frac{-5}{4}\right)\)
3 \(\left(\frac{3}{3}, \infty\right)\)
4 \(\left(-\infty, \frac{-5}{4}\right) \cup\left(\frac{3}{4},-\infty\right)\)
AP EAMCET-2017
Sets, Relation and Function

117406 Let \(A=\{-4,-2,-1,0,3,5\}, f: A \rightarrow I R \quad\) be defined by
\(f(x)=\left\{\begin{array}{ccc}\mathbf{3 x}-1 & \text { for } & \mathbf{x}>\mathbf{3} \\ \mathbf{x}^2+1 & \text { for } & -\mathbf{3} \leq \mathbf{x} \leq \mathbf{3} \\ \mathbf{2 x}-\mathbf{3} & \text { for } & \mathbf{x}\lt -\mathbf{3}\end{array}\right.\)
Then the range of \(f\) is

1 \(\{-11,5,2,1,10,14\}\)
2 \(\{-11,-2,2,1,8,14\}\)
3 \(\{-11,5,2,1,8,14\}\)
4 \(\{-11,-7,-5,1,10,14\}\)
AP EAMCET-2017
Sets, Relation and Function

117407 The range of the function \(f(x)=\frac{x}{x^2-5 x+9}\) is

1 \(\left[\frac{1}{11}, 1\right]\)
2 \(\left[\frac{-1}{11}, 1\right]\)
3 \(\left[-1, \frac{-1}{11}\right]\)
4 \(\left[-1, \frac{1}{11}\right]\)
AP EAMCET-08.07.2022
Sets, Relation and Function

117408 The domain of the real valued function \(f(x)=\) \(\sqrt{\frac{\mathbf{2 - | x |}}{\mathbf{3}-|\mathbf{x}|}}\) is

1 \((-\infty, \infty)\)
2 \((-\infty,-3) \cup(2, \infty)\)
3 \((-\infty,-3) \cup(-2,2) \cup[3, \infty)\)
4 \((-\infty,-3) \cup[-2,2] \cup(3, \infty)\)
AP EAMCET-08.07.2022
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Sets, Relation and Function

117405 \(\frac{x-1}{3 x+4}\lt \frac{x-3}{3 x-2}\) holds, for all \(x\) in the interval

1 \(\left(\frac{-4}{3}, \frac{2}{3}\right)\)
2 \(\left(-\infty, \frac{-5}{4}\right)\)
3 \(\left(\frac{3}{3}, \infty\right)\)
4 \(\left(-\infty, \frac{-5}{4}\right) \cup\left(\frac{3}{4},-\infty\right)\)
AP EAMCET-2017
Sets, Relation and Function

117406 Let \(A=\{-4,-2,-1,0,3,5\}, f: A \rightarrow I R \quad\) be defined by
\(f(x)=\left\{\begin{array}{ccc}\mathbf{3 x}-1 & \text { for } & \mathbf{x}>\mathbf{3} \\ \mathbf{x}^2+1 & \text { for } & -\mathbf{3} \leq \mathbf{x} \leq \mathbf{3} \\ \mathbf{2 x}-\mathbf{3} & \text { for } & \mathbf{x}\lt -\mathbf{3}\end{array}\right.\)
Then the range of \(f\) is

1 \(\{-11,5,2,1,10,14\}\)
2 \(\{-11,-2,2,1,8,14\}\)
3 \(\{-11,5,2,1,8,14\}\)
4 \(\{-11,-7,-5,1,10,14\}\)
AP EAMCET-2017
Sets, Relation and Function

117407 The range of the function \(f(x)=\frac{x}{x^2-5 x+9}\) is

1 \(\left[\frac{1}{11}, 1\right]\)
2 \(\left[\frac{-1}{11}, 1\right]\)
3 \(\left[-1, \frac{-1}{11}\right]\)
4 \(\left[-1, \frac{1}{11}\right]\)
AP EAMCET-08.07.2022
Sets, Relation and Function

117408 The domain of the real valued function \(f(x)=\) \(\sqrt{\frac{\mathbf{2 - | x |}}{\mathbf{3}-|\mathbf{x}|}}\) is

1 \((-\infty, \infty)\)
2 \((-\infty,-3) \cup(2, \infty)\)
3 \((-\infty,-3) \cup(-2,2) \cup[3, \infty)\)
4 \((-\infty,-3) \cup[-2,2] \cup(3, \infty)\)
AP EAMCET-08.07.2022
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