Types of Functions
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Sets, Relation and Function

117041 Given that a function \(f(x)=[x]^2+x^2\), where \([x]\) is the greatest integer less than or equal to \(x\), If \(f(x)>25\), then the value of \(x\) is

1 any real number
2 a member of the set \(\{x \mid x>0\}\)
3 a member of the set \(\{x \mid x \leq-4\) or \(x \geq 4\}\)
4 a member of the set \(\{x \mid x>25\) or \(x \leq 0\}\)
Sets, Relation and Function

117042 Let \(f: R \rightarrow R\) be defined by
\(\mathbf{f}(\mathbf{x})=\left\{\begin{array}{ccc}\mathbf{2 x} & ; & \mathbf{x}>\mathbf{3} \\ \mathbf{x}^2 & ; & \mathbf{1}\lt \mathbf{x} \leq \mathbf{3} \\ \mathbf{3 x} & ; & \mathbf{x} \leq \mathbf{1}\end{array}\right.\)
Then \(\mathbf{f}(-\mathbf{1})+\mathbf{f}(\mathbf{2})+\mathbf{f}(\mathbf{4})\) is

1 9
2 14
3 5
4 10
Sets, Relation and Function

117043 Function \(f: \mathrm{N}, f(\mathrm{x})=2 \mathrm{x}+3\) is

1 many-one onto function
2 many-one into function
3 one-one onto function
4 one-one into function
Sets, Relation and Function

117045 The range of the function \(f(x)=\sin [x]\), \(-\frac{\pi}{4}\lt x\lt \frac{\pi}{4}\) where \([x]\) denotes the greatest integer \(\leq x\), is

1 \(\{0\}\)
2 \(\{0,-1\}\)
3 \(\{0, \pm \sin 1\}\)
4 \(\{0,-\sin 1\}\)
Sets, Relation and Function

117041 Given that a function \(f(x)=[x]^2+x^2\), where \([x]\) is the greatest integer less than or equal to \(x\), If \(f(x)>25\), then the value of \(x\) is

1 any real number
2 a member of the set \(\{x \mid x>0\}\)
3 a member of the set \(\{x \mid x \leq-4\) or \(x \geq 4\}\)
4 a member of the set \(\{x \mid x>25\) or \(x \leq 0\}\)
Sets, Relation and Function

117042 Let \(f: R \rightarrow R\) be defined by
\(\mathbf{f}(\mathbf{x})=\left\{\begin{array}{ccc}\mathbf{2 x} & ; & \mathbf{x}>\mathbf{3} \\ \mathbf{x}^2 & ; & \mathbf{1}\lt \mathbf{x} \leq \mathbf{3} \\ \mathbf{3 x} & ; & \mathbf{x} \leq \mathbf{1}\end{array}\right.\)
Then \(\mathbf{f}(-\mathbf{1})+\mathbf{f}(\mathbf{2})+\mathbf{f}(\mathbf{4})\) is

1 9
2 14
3 5
4 10
Sets, Relation and Function

117043 Function \(f: \mathrm{N}, f(\mathrm{x})=2 \mathrm{x}+3\) is

1 many-one onto function
2 many-one into function
3 one-one onto function
4 one-one into function
Sets, Relation and Function

117045 The range of the function \(f(x)=\sin [x]\), \(-\frac{\pi}{4}\lt x\lt \frac{\pi}{4}\) where \([x]\) denotes the greatest integer \(\leq x\), is

1 \(\{0\}\)
2 \(\{0,-1\}\)
3 \(\{0, \pm \sin 1\}\)
4 \(\{0,-\sin 1\}\)
Sets, Relation and Function

117041 Given that a function \(f(x)=[x]^2+x^2\), where \([x]\) is the greatest integer less than or equal to \(x\), If \(f(x)>25\), then the value of \(x\) is

1 any real number
2 a member of the set \(\{x \mid x>0\}\)
3 a member of the set \(\{x \mid x \leq-4\) or \(x \geq 4\}\)
4 a member of the set \(\{x \mid x>25\) or \(x \leq 0\}\)
Sets, Relation and Function

117042 Let \(f: R \rightarrow R\) be defined by
\(\mathbf{f}(\mathbf{x})=\left\{\begin{array}{ccc}\mathbf{2 x} & ; & \mathbf{x}>\mathbf{3} \\ \mathbf{x}^2 & ; & \mathbf{1}\lt \mathbf{x} \leq \mathbf{3} \\ \mathbf{3 x} & ; & \mathbf{x} \leq \mathbf{1}\end{array}\right.\)
Then \(\mathbf{f}(-\mathbf{1})+\mathbf{f}(\mathbf{2})+\mathbf{f}(\mathbf{4})\) is

1 9
2 14
3 5
4 10
Sets, Relation and Function

117043 Function \(f: \mathrm{N}, f(\mathrm{x})=2 \mathrm{x}+3\) is

1 many-one onto function
2 many-one into function
3 one-one onto function
4 one-one into function
Sets, Relation and Function

117045 The range of the function \(f(x)=\sin [x]\), \(-\frac{\pi}{4}\lt x\lt \frac{\pi}{4}\) where \([x]\) denotes the greatest integer \(\leq x\), is

1 \(\{0\}\)
2 \(\{0,-1\}\)
3 \(\{0, \pm \sin 1\}\)
4 \(\{0,-\sin 1\}\)
Sets, Relation and Function

117041 Given that a function \(f(x)=[x]^2+x^2\), where \([x]\) is the greatest integer less than or equal to \(x\), If \(f(x)>25\), then the value of \(x\) is

1 any real number
2 a member of the set \(\{x \mid x>0\}\)
3 a member of the set \(\{x \mid x \leq-4\) or \(x \geq 4\}\)
4 a member of the set \(\{x \mid x>25\) or \(x \leq 0\}\)
Sets, Relation and Function

117042 Let \(f: R \rightarrow R\) be defined by
\(\mathbf{f}(\mathbf{x})=\left\{\begin{array}{ccc}\mathbf{2 x} & ; & \mathbf{x}>\mathbf{3} \\ \mathbf{x}^2 & ; & \mathbf{1}\lt \mathbf{x} \leq \mathbf{3} \\ \mathbf{3 x} & ; & \mathbf{x} \leq \mathbf{1}\end{array}\right.\)
Then \(\mathbf{f}(-\mathbf{1})+\mathbf{f}(\mathbf{2})+\mathbf{f}(\mathbf{4})\) is

1 9
2 14
3 5
4 10
Sets, Relation and Function

117043 Function \(f: \mathrm{N}, f(\mathrm{x})=2 \mathrm{x}+3\) is

1 many-one onto function
2 many-one into function
3 one-one onto function
4 one-one into function
Sets, Relation and Function

117045 The range of the function \(f(x)=\sin [x]\), \(-\frac{\pi}{4}\lt x\lt \frac{\pi}{4}\) where \([x]\) denotes the greatest integer \(\leq x\), is

1 \(\{0\}\)
2 \(\{0,-1\}\)
3 \(\{0, \pm \sin 1\}\)
4 \(\{0,-\sin 1\}\)