Types of Functions
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Sets, Relation and Function

117083 Let \(\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}\) defined by \(\mathrm{f}(\mathrm{x})=\mathbf{5 x ^ { 4 } + 2 \text { . Then }}\)

1 \(f\) is one-one but not onto
2 \(f\) is onto but not one-one
3 \(f\) is both one-one and onto
4 \(f\) is neither one-one nor onto
Shift-I
Sets, Relation and Function

117084 If \(F: R \rightarrow R\) is defined as \(f(x)=x^2-2 x-3\) then \(f\) is

1 one-one but not onto
2 onto but not one-one
3 neither one-one onto
4 a bijection
Shift-I
Sets, Relation and Function

117085 Let \(f:(-1,1) \rightarrow B\) is defined as \(f(x)=\tan ^{-1}\) \(\frac{2 x}{1-x^2}\). Function \(f\) is one-one and onto, then the interval \(B\) is

1 \(\left(0, \frac{\pi}{2}\right)\)
2 \(\left[0, \frac{\pi}{2}\right)\)
3 \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\)
4 \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
Rajasthan PET-2007
Sets, Relation and Function

117087 Let \(\mathrm{N}\) be the set of all natural numbers, \(\mathrm{Z}\) be the set of all integers and \(\sigma: N \rightarrow Z\) be defined by
\(\sigma(n)=\left\{\begin{array}{l}\frac{n}{2}, \text { if nis even } \\ -\frac{n-1}{2} \text {, if nis odd }\end{array}\right.\) then

1 \(\sigma\) is onto but not one-one
2 \(\sigma\) is one-one but not onto
3 \(\sigma\) is neither one-one nor onto
4 \(\sigma\) is one-one and onto
AP EAMCET-23 April 2018. Shift-I
Sets, Relation and Function

117088 If the function \(f: R \rightarrow\) is defined by \(f(x)=x|x|\), then

1 \(f\) is one-one but not onto
2 \(f\) is onto but not one-one
3 \(f\) is both one-one and onto
4 \(f\) is neither one-one nor onto
Shift-II
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Sets, Relation and Function

117083 Let \(\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}\) defined by \(\mathrm{f}(\mathrm{x})=\mathbf{5 x ^ { 4 } + 2 \text { . Then }}\)

1 \(f\) is one-one but not onto
2 \(f\) is onto but not one-one
3 \(f\) is both one-one and onto
4 \(f\) is neither one-one nor onto
Shift-I
Sets, Relation and Function

117084 If \(F: R \rightarrow R\) is defined as \(f(x)=x^2-2 x-3\) then \(f\) is

1 one-one but not onto
2 onto but not one-one
3 neither one-one onto
4 a bijection
Shift-I
Sets, Relation and Function

117085 Let \(f:(-1,1) \rightarrow B\) is defined as \(f(x)=\tan ^{-1}\) \(\frac{2 x}{1-x^2}\). Function \(f\) is one-one and onto, then the interval \(B\) is

1 \(\left(0, \frac{\pi}{2}\right)\)
2 \(\left[0, \frac{\pi}{2}\right)\)
3 \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\)
4 \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
Rajasthan PET-2007
Sets, Relation and Function

117087 Let \(\mathrm{N}\) be the set of all natural numbers, \(\mathrm{Z}\) be the set of all integers and \(\sigma: N \rightarrow Z\) be defined by
\(\sigma(n)=\left\{\begin{array}{l}\frac{n}{2}, \text { if nis even } \\ -\frac{n-1}{2} \text {, if nis odd }\end{array}\right.\) then

1 \(\sigma\) is onto but not one-one
2 \(\sigma\) is one-one but not onto
3 \(\sigma\) is neither one-one nor onto
4 \(\sigma\) is one-one and onto
AP EAMCET-23 April 2018. Shift-I
Sets, Relation and Function

117088 If the function \(f: R \rightarrow\) is defined by \(f(x)=x|x|\), then

1 \(f\) is one-one but not onto
2 \(f\) is onto but not one-one
3 \(f\) is both one-one and onto
4 \(f\) is neither one-one nor onto
Shift-II
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Sets, Relation and Function

117083 Let \(\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}\) defined by \(\mathrm{f}(\mathrm{x})=\mathbf{5 x ^ { 4 } + 2 \text { . Then }}\)

1 \(f\) is one-one but not onto
2 \(f\) is onto but not one-one
3 \(f\) is both one-one and onto
4 \(f\) is neither one-one nor onto
Shift-I
Sets, Relation and Function

117084 If \(F: R \rightarrow R\) is defined as \(f(x)=x^2-2 x-3\) then \(f\) is

1 one-one but not onto
2 onto but not one-one
3 neither one-one onto
4 a bijection
Shift-I
Sets, Relation and Function

117085 Let \(f:(-1,1) \rightarrow B\) is defined as \(f(x)=\tan ^{-1}\) \(\frac{2 x}{1-x^2}\). Function \(f\) is one-one and onto, then the interval \(B\) is

1 \(\left(0, \frac{\pi}{2}\right)\)
2 \(\left[0, \frac{\pi}{2}\right)\)
3 \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\)
4 \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
Rajasthan PET-2007
Sets, Relation and Function

117087 Let \(\mathrm{N}\) be the set of all natural numbers, \(\mathrm{Z}\) be the set of all integers and \(\sigma: N \rightarrow Z\) be defined by
\(\sigma(n)=\left\{\begin{array}{l}\frac{n}{2}, \text { if nis even } \\ -\frac{n-1}{2} \text {, if nis odd }\end{array}\right.\) then

1 \(\sigma\) is onto but not one-one
2 \(\sigma\) is one-one but not onto
3 \(\sigma\) is neither one-one nor onto
4 \(\sigma\) is one-one and onto
AP EAMCET-23 April 2018. Shift-I
Sets, Relation and Function

117088 If the function \(f: R \rightarrow\) is defined by \(f(x)=x|x|\), then

1 \(f\) is one-one but not onto
2 \(f\) is onto but not one-one
3 \(f\) is both one-one and onto
4 \(f\) is neither one-one nor onto
Shift-II
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Sets, Relation and Function

117083 Let \(\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}\) defined by \(\mathrm{f}(\mathrm{x})=\mathbf{5 x ^ { 4 } + 2 \text { . Then }}\)

1 \(f\) is one-one but not onto
2 \(f\) is onto but not one-one
3 \(f\) is both one-one and onto
4 \(f\) is neither one-one nor onto
Shift-I
Sets, Relation and Function

117084 If \(F: R \rightarrow R\) is defined as \(f(x)=x^2-2 x-3\) then \(f\) is

1 one-one but not onto
2 onto but not one-one
3 neither one-one onto
4 a bijection
Shift-I
Sets, Relation and Function

117085 Let \(f:(-1,1) \rightarrow B\) is defined as \(f(x)=\tan ^{-1}\) \(\frac{2 x}{1-x^2}\). Function \(f\) is one-one and onto, then the interval \(B\) is

1 \(\left(0, \frac{\pi}{2}\right)\)
2 \(\left[0, \frac{\pi}{2}\right)\)
3 \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\)
4 \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
Rajasthan PET-2007
Sets, Relation and Function

117087 Let \(\mathrm{N}\) be the set of all natural numbers, \(\mathrm{Z}\) be the set of all integers and \(\sigma: N \rightarrow Z\) be defined by
\(\sigma(n)=\left\{\begin{array}{l}\frac{n}{2}, \text { if nis even } \\ -\frac{n-1}{2} \text {, if nis odd }\end{array}\right.\) then

1 \(\sigma\) is onto but not one-one
2 \(\sigma\) is one-one but not onto
3 \(\sigma\) is neither one-one nor onto
4 \(\sigma\) is one-one and onto
AP EAMCET-23 April 2018. Shift-I
Sets, Relation and Function

117088 If the function \(f: R \rightarrow\) is defined by \(f(x)=x|x|\), then

1 \(f\) is one-one but not onto
2 \(f\) is onto but not one-one
3 \(f\) is both one-one and onto
4 \(f\) is neither one-one nor onto
Shift-II
Join With Us for More Updates
Sets, Relation and Function

117083 Let \(\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}\) defined by \(\mathrm{f}(\mathrm{x})=\mathbf{5 x ^ { 4 } + 2 \text { . Then }}\)

1 \(f\) is one-one but not onto
2 \(f\) is onto but not one-one
3 \(f\) is both one-one and onto
4 \(f\) is neither one-one nor onto
Shift-I
Sets, Relation and Function

117084 If \(F: R \rightarrow R\) is defined as \(f(x)=x^2-2 x-3\) then \(f\) is

1 one-one but not onto
2 onto but not one-one
3 neither one-one onto
4 a bijection
Shift-I
Sets, Relation and Function

117085 Let \(f:(-1,1) \rightarrow B\) is defined as \(f(x)=\tan ^{-1}\) \(\frac{2 x}{1-x^2}\). Function \(f\) is one-one and onto, then the interval \(B\) is

1 \(\left(0, \frac{\pi}{2}\right)\)
2 \(\left[0, \frac{\pi}{2}\right)\)
3 \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\)
4 \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
Rajasthan PET-2007
Sets, Relation and Function

117087 Let \(\mathrm{N}\) be the set of all natural numbers, \(\mathrm{Z}\) be the set of all integers and \(\sigma: N \rightarrow Z\) be defined by
\(\sigma(n)=\left\{\begin{array}{l}\frac{n}{2}, \text { if nis even } \\ -\frac{n-1}{2} \text {, if nis odd }\end{array}\right.\) then

1 \(\sigma\) is onto but not one-one
2 \(\sigma\) is one-one but not onto
3 \(\sigma\) is neither one-one nor onto
4 \(\sigma\) is one-one and onto
AP EAMCET-23 April 2018. Shift-I
Sets, Relation and Function

117088 If the function \(f: R \rightarrow\) is defined by \(f(x)=x|x|\), then

1 \(f\) is one-one but not onto
2 \(f\) is onto but not one-one
3 \(f\) is both one-one and onto
4 \(f\) is neither one-one nor onto
Shift-II