Inverse of Function and Binary Operation
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Sets, Relation and Function

117140 Let \(f: N \rightarrow Y\) ( \(N\) is the set of natural numbers) defined as \(f(x)=4 x+3\) where \(Y=\{y \in N ; y=\) \(4 x+3\) for some \(x \in N\}\)
Then the inverse of \(f(x)\) is equal to

1 \(g(y)=\frac{3 y+4}{3}\)
2 \(g(y)=4+\frac{y+3}{4}\)
3 \(g(y)=\frac{y+3}{4}\)
4 \(g(y)=\frac{y-3}{4}\)
[SRMJEEE-2016]
Sets, Relation and Function

117141 Consider the following statements :

1 1 only
2 2 only
3 Both 1 and 2
4 Neither 1 nor 2
[SCRA-2010]
Sets, Relation and Function

117142 Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be defined as \(f(x)=\mathbf{x}^2+1\), find \(f^{-1}(-5)\).

1 \(\{\phi\}\)
2 \(\phi\)
3 \(\{5\}\)
4 \(\{-5,5\}\)
[VITEEE-2011]
Sets, Relation and Function

117143 In a group \((G, *)\), then equation \(x * a=b\) has a

1 unique solution \(\mathrm{b} * \mathrm{a}^{-1}\)
2 unique solution \(\mathrm{a}^{-1} * \mathrm{~b}\)
3 unique solution \(\mathrm{a}^{-1} * \mathrm{~b}^{-1}\)
4 many solutions
[VITEEE-2011]
Sets, Relation and Function

117136 The function \(f: R \rightarrow R\) given by \(f(x)=7-3 x\) is

1 not one-one
2 not onto
3 even
4 one-one and onto
5 odd
[Kerala CEE-2021]
Join With Us for More Updates
Sets, Relation and Function

117140 Let \(f: N \rightarrow Y\) ( \(N\) is the set of natural numbers) defined as \(f(x)=4 x+3\) where \(Y=\{y \in N ; y=\) \(4 x+3\) for some \(x \in N\}\)
Then the inverse of \(f(x)\) is equal to

1 \(g(y)=\frac{3 y+4}{3}\)
2 \(g(y)=4+\frac{y+3}{4}\)
3 \(g(y)=\frac{y+3}{4}\)
4 \(g(y)=\frac{y-3}{4}\)
[SRMJEEE-2016]
Sets, Relation and Function

117141 Consider the following statements :

1 1 only
2 2 only
3 Both 1 and 2
4 Neither 1 nor 2
[SCRA-2010]
Sets, Relation and Function

117142 Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be defined as \(f(x)=\mathbf{x}^2+1\), find \(f^{-1}(-5)\).

1 \(\{\phi\}\)
2 \(\phi\)
3 \(\{5\}\)
4 \(\{-5,5\}\)
[VITEEE-2011]
Sets, Relation and Function

117143 In a group \((G, *)\), then equation \(x * a=b\) has a

1 unique solution \(\mathrm{b} * \mathrm{a}^{-1}\)
2 unique solution \(\mathrm{a}^{-1} * \mathrm{~b}\)
3 unique solution \(\mathrm{a}^{-1} * \mathrm{~b}^{-1}\)
4 many solutions
[VITEEE-2011]
Sets, Relation and Function

117136 The function \(f: R \rightarrow R\) given by \(f(x)=7-3 x\) is

1 not one-one
2 not onto
3 even
4 one-one and onto
5 odd
[Kerala CEE-2021]
For More Updates join with Us
Sets, Relation and Function

117140 Let \(f: N \rightarrow Y\) ( \(N\) is the set of natural numbers) defined as \(f(x)=4 x+3\) where \(Y=\{y \in N ; y=\) \(4 x+3\) for some \(x \in N\}\)
Then the inverse of \(f(x)\) is equal to

1 \(g(y)=\frac{3 y+4}{3}\)
2 \(g(y)=4+\frac{y+3}{4}\)
3 \(g(y)=\frac{y+3}{4}\)
4 \(g(y)=\frac{y-3}{4}\)
[SRMJEEE-2016]
Sets, Relation and Function

117141 Consider the following statements :

1 1 only
2 2 only
3 Both 1 and 2
4 Neither 1 nor 2
[SCRA-2010]
Sets, Relation and Function

117142 Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be defined as \(f(x)=\mathbf{x}^2+1\), find \(f^{-1}(-5)\).

1 \(\{\phi\}\)
2 \(\phi\)
3 \(\{5\}\)
4 \(\{-5,5\}\)
[VITEEE-2011]
Sets, Relation and Function

117143 In a group \((G, *)\), then equation \(x * a=b\) has a

1 unique solution \(\mathrm{b} * \mathrm{a}^{-1}\)
2 unique solution \(\mathrm{a}^{-1} * \mathrm{~b}\)
3 unique solution \(\mathrm{a}^{-1} * \mathrm{~b}^{-1}\)
4 many solutions
[VITEEE-2011]
Sets, Relation and Function

117136 The function \(f: R \rightarrow R\) given by \(f(x)=7-3 x\) is

1 not one-one
2 not onto
3 even
4 one-one and onto
5 odd
[Kerala CEE-2021]
NEET DIGITAL LIBRARY
Sets, Relation and Function

117140 Let \(f: N \rightarrow Y\) ( \(N\) is the set of natural numbers) defined as \(f(x)=4 x+3\) where \(Y=\{y \in N ; y=\) \(4 x+3\) for some \(x \in N\}\)
Then the inverse of \(f(x)\) is equal to

1 \(g(y)=\frac{3 y+4}{3}\)
2 \(g(y)=4+\frac{y+3}{4}\)
3 \(g(y)=\frac{y+3}{4}\)
4 \(g(y)=\frac{y-3}{4}\)
[SRMJEEE-2016]
Sets, Relation and Function

117141 Consider the following statements :

1 1 only
2 2 only
3 Both 1 and 2
4 Neither 1 nor 2
[SCRA-2010]
Sets, Relation and Function

117142 Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be defined as \(f(x)=\mathbf{x}^2+1\), find \(f^{-1}(-5)\).

1 \(\{\phi\}\)
2 \(\phi\)
3 \(\{5\}\)
4 \(\{-5,5\}\)
[VITEEE-2011]
Sets, Relation and Function

117143 In a group \((G, *)\), then equation \(x * a=b\) has a

1 unique solution \(\mathrm{b} * \mathrm{a}^{-1}\)
2 unique solution \(\mathrm{a}^{-1} * \mathrm{~b}\)
3 unique solution \(\mathrm{a}^{-1} * \mathrm{~b}^{-1}\)
4 many solutions
[VITEEE-2011]
Sets, Relation and Function

117136 The function \(f: R \rightarrow R\) given by \(f(x)=7-3 x\) is

1 not one-one
2 not onto
3 even
4 one-one and onto
5 odd
[Kerala CEE-2021]
Join With Us for More Updates
Sets, Relation and Function

117140 Let \(f: N \rightarrow Y\) ( \(N\) is the set of natural numbers) defined as \(f(x)=4 x+3\) where \(Y=\{y \in N ; y=\) \(4 x+3\) for some \(x \in N\}\)
Then the inverse of \(f(x)\) is equal to

1 \(g(y)=\frac{3 y+4}{3}\)
2 \(g(y)=4+\frac{y+3}{4}\)
3 \(g(y)=\frac{y+3}{4}\)
4 \(g(y)=\frac{y-3}{4}\)
[SRMJEEE-2016]
Sets, Relation and Function

117141 Consider the following statements :

1 1 only
2 2 only
3 Both 1 and 2
4 Neither 1 nor 2
[SCRA-2010]
Sets, Relation and Function

117142 Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be defined as \(f(x)=\mathbf{x}^2+1\), find \(f^{-1}(-5)\).

1 \(\{\phi\}\)
2 \(\phi\)
3 \(\{5\}\)
4 \(\{-5,5\}\)
[VITEEE-2011]
Sets, Relation and Function

117143 In a group \((G, *)\), then equation \(x * a=b\) has a

1 unique solution \(\mathrm{b} * \mathrm{a}^{-1}\)
2 unique solution \(\mathrm{a}^{-1} * \mathrm{~b}\)
3 unique solution \(\mathrm{a}^{-1} * \mathrm{~b}^{-1}\)
4 many solutions
[VITEEE-2011]
Sets, Relation and Function

117136 The function \(f: R \rightarrow R\) given by \(f(x)=7-3 x\) is

1 not one-one
2 not onto
3 even
4 one-one and onto
5 odd
[Kerala CEE-2021]