Types of Functions
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Sets, Relation and Function

117101 The function \(f:[0, \infty) \rightarrow[0, \infty)\) defined by \(f(x)\) \(=\frac{2 \mathbf{x}}{1+2 \mathbf{x}}\) is

1 One-one and onto
2 One-one but not onto
3 Not one-one but onto
4 neither one-one nor onto
[J and K CET-2011]
Sets, Relation and Function

117102 The function \(f: R \rightarrow R\) is given by \(f(x)=x^3-1\) is

1 A one-one function
2 An onto function
3 A bijection
4 neither one-one nor onto
[J and K CET-2008]
Sets, Relation and Function

117103 For real \(x\), let \(f(x)=x^3+5 x+1\), then

1 \(f\) is one -one but not onto \(R\)
2 \(f\) is onto \(R\) but not one- one
3 \(f\) is one - one and onto \(R\)
4 \(f\) is neither one -one nor onto \(R\)
[AIEEE-2009]
Sets, Relation and Function

117104 Let \(\mathbf{A}=\{\mathbf{x} \in \mathbf{R}: \mathbf{x}\) is not a positive integer \(\}\).
Define a function \(f: A \rightarrow R\) as \(f(x)=\frac{2 x}{x-1}\), then
\(f\) is

1 Injective but not surjective.
2 Not injective.
3 Surjective but not injective.
4 Neither injective nor surjective.
[JEE Main 09.01.2019 Shift-II]
Sets, Relation and Function

117105 Let \(\mathrm{N}\) be the set of natural numbers and two functions \(f\) and \(g\) be defined as \(f, g: N \rightarrow N\) such that
\(f(n)= \begin{cases}\frac{n+1}{2} \text { if nis odd } \\ \frac{n}{2} \text { if nis even }\end{cases}\)
and \(g(n)=n-(-1)^n\). Then fog is

1 one-one but not onto
2 onto but not one-one
3 both one-one and onto
4 neither one-one nor onto
[JEE Main 10.01.2019 Shift - II
NEET DIGITAL LIBRARY
Sets, Relation and Function

117101 The function \(f:[0, \infty) \rightarrow[0, \infty)\) defined by \(f(x)\) \(=\frac{2 \mathbf{x}}{1+2 \mathbf{x}}\) is

1 One-one and onto
2 One-one but not onto
3 Not one-one but onto
4 neither one-one nor onto
[J and K CET-2011]
Sets, Relation and Function

117102 The function \(f: R \rightarrow R\) is given by \(f(x)=x^3-1\) is

1 A one-one function
2 An onto function
3 A bijection
4 neither one-one nor onto
[J and K CET-2008]
Sets, Relation and Function

117103 For real \(x\), let \(f(x)=x^3+5 x+1\), then

1 \(f\) is one -one but not onto \(R\)
2 \(f\) is onto \(R\) but not one- one
3 \(f\) is one - one and onto \(R\)
4 \(f\) is neither one -one nor onto \(R\)
[AIEEE-2009]
Sets, Relation and Function

117104 Let \(\mathbf{A}=\{\mathbf{x} \in \mathbf{R}: \mathbf{x}\) is not a positive integer \(\}\).
Define a function \(f: A \rightarrow R\) as \(f(x)=\frac{2 x}{x-1}\), then
\(f\) is

1 Injective but not surjective.
2 Not injective.
3 Surjective but not injective.
4 Neither injective nor surjective.
[JEE Main 09.01.2019 Shift-II]
Sets, Relation and Function

117105 Let \(\mathrm{N}\) be the set of natural numbers and two functions \(f\) and \(g\) be defined as \(f, g: N \rightarrow N\) such that
\(f(n)= \begin{cases}\frac{n+1}{2} \text { if nis odd } \\ \frac{n}{2} \text { if nis even }\end{cases}\)
and \(g(n)=n-(-1)^n\). Then fog is

1 one-one but not onto
2 onto but not one-one
3 both one-one and onto
4 neither one-one nor onto
[JEE Main 10.01.2019 Shift - II
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Sets, Relation and Function

117101 The function \(f:[0, \infty) \rightarrow[0, \infty)\) defined by \(f(x)\) \(=\frac{2 \mathbf{x}}{1+2 \mathbf{x}}\) is

1 One-one and onto
2 One-one but not onto
3 Not one-one but onto
4 neither one-one nor onto
[J and K CET-2011]
Sets, Relation and Function

117102 The function \(f: R \rightarrow R\) is given by \(f(x)=x^3-1\) is

1 A one-one function
2 An onto function
3 A bijection
4 neither one-one nor onto
[J and K CET-2008]
Sets, Relation and Function

117103 For real \(x\), let \(f(x)=x^3+5 x+1\), then

1 \(f\) is one -one but not onto \(R\)
2 \(f\) is onto \(R\) but not one- one
3 \(f\) is one - one and onto \(R\)
4 \(f\) is neither one -one nor onto \(R\)
[AIEEE-2009]
Sets, Relation and Function

117104 Let \(\mathbf{A}=\{\mathbf{x} \in \mathbf{R}: \mathbf{x}\) is not a positive integer \(\}\).
Define a function \(f: A \rightarrow R\) as \(f(x)=\frac{2 x}{x-1}\), then
\(f\) is

1 Injective but not surjective.
2 Not injective.
3 Surjective but not injective.
4 Neither injective nor surjective.
[JEE Main 09.01.2019 Shift-II]
Sets, Relation and Function

117105 Let \(\mathrm{N}\) be the set of natural numbers and two functions \(f\) and \(g\) be defined as \(f, g: N \rightarrow N\) such that
\(f(n)= \begin{cases}\frac{n+1}{2} \text { if nis odd } \\ \frac{n}{2} \text { if nis even }\end{cases}\)
and \(g(n)=n-(-1)^n\). Then fog is

1 one-one but not onto
2 onto but not one-one
3 both one-one and onto
4 neither one-one nor onto
[JEE Main 10.01.2019 Shift - II
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Sets, Relation and Function

117101 The function \(f:[0, \infty) \rightarrow[0, \infty)\) defined by \(f(x)\) \(=\frac{2 \mathbf{x}}{1+2 \mathbf{x}}\) is

1 One-one and onto
2 One-one but not onto
3 Not one-one but onto
4 neither one-one nor onto
[J and K CET-2011]
Sets, Relation and Function

117102 The function \(f: R \rightarrow R\) is given by \(f(x)=x^3-1\) is

1 A one-one function
2 An onto function
3 A bijection
4 neither one-one nor onto
[J and K CET-2008]
Sets, Relation and Function

117103 For real \(x\), let \(f(x)=x^3+5 x+1\), then

1 \(f\) is one -one but not onto \(R\)
2 \(f\) is onto \(R\) but not one- one
3 \(f\) is one - one and onto \(R\)
4 \(f\) is neither one -one nor onto \(R\)
[AIEEE-2009]
Sets, Relation and Function

117104 Let \(\mathbf{A}=\{\mathbf{x} \in \mathbf{R}: \mathbf{x}\) is not a positive integer \(\}\).
Define a function \(f: A \rightarrow R\) as \(f(x)=\frac{2 x}{x-1}\), then
\(f\) is

1 Injective but not surjective.
2 Not injective.
3 Surjective but not injective.
4 Neither injective nor surjective.
[JEE Main 09.01.2019 Shift-II]
Sets, Relation and Function

117105 Let \(\mathrm{N}\) be the set of natural numbers and two functions \(f\) and \(g\) be defined as \(f, g: N \rightarrow N\) such that
\(f(n)= \begin{cases}\frac{n+1}{2} \text { if nis odd } \\ \frac{n}{2} \text { if nis even }\end{cases}\)
and \(g(n)=n-(-1)^n\). Then fog is

1 one-one but not onto
2 onto but not one-one
3 both one-one and onto
4 neither one-one nor onto
[JEE Main 10.01.2019 Shift - II
NEET DIGITAL LIBRARY
Sets, Relation and Function

117101 The function \(f:[0, \infty) \rightarrow[0, \infty)\) defined by \(f(x)\) \(=\frac{2 \mathbf{x}}{1+2 \mathbf{x}}\) is

1 One-one and onto
2 One-one but not onto
3 Not one-one but onto
4 neither one-one nor onto
[J and K CET-2011]
Sets, Relation and Function

117102 The function \(f: R \rightarrow R\) is given by \(f(x)=x^3-1\) is

1 A one-one function
2 An onto function
3 A bijection
4 neither one-one nor onto
[J and K CET-2008]
Sets, Relation and Function

117103 For real \(x\), let \(f(x)=x^3+5 x+1\), then

1 \(f\) is one -one but not onto \(R\)
2 \(f\) is onto \(R\) but not one- one
3 \(f\) is one - one and onto \(R\)
4 \(f\) is neither one -one nor onto \(R\)
[AIEEE-2009]
Sets, Relation and Function

117104 Let \(\mathbf{A}=\{\mathbf{x} \in \mathbf{R}: \mathbf{x}\) is not a positive integer \(\}\).
Define a function \(f: A \rightarrow R\) as \(f(x)=\frac{2 x}{x-1}\), then
\(f\) is

1 Injective but not surjective.
2 Not injective.
3 Surjective but not injective.
4 Neither injective nor surjective.
[JEE Main 09.01.2019 Shift-II]
Sets, Relation and Function

117105 Let \(\mathrm{N}\) be the set of natural numbers and two functions \(f\) and \(g\) be defined as \(f, g: N \rightarrow N\) such that
\(f(n)= \begin{cases}\frac{n+1}{2} \text { if nis odd } \\ \frac{n}{2} \text { if nis even }\end{cases}\)
and \(g(n)=n-(-1)^n\). Then fog is

1 one-one but not onto
2 onto but not one-one
3 both one-one and onto
4 neither one-one nor onto
[JEE Main 10.01.2019 Shift - II