117093 If \(f: N \rightarrow R\) is defined by \(f(1)=-1\) and \(f(n+1)\) \(=3 \mathrm{f}(\mathrm{n})+\mathbf{2}\) for \(n \geq 1\) then \(f\) is

117094 Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) and \(\mathbf{g}: \mathbf{R} \rightarrow \mathbf{R}\) be the functions defined by
\(f(x)=\frac{x}{1+x^2}, x \in R, g(x)=\frac{x^2}{1+x^2}, x \in I R\)
Then, the correct statement (s) among the following is/are
A : Both \(f, g\) are one-one
B :Both \(f, g\) are onto
C : Both \(f, g\) are not one-one as well as not onto
\(\mathrm{D}: \boldsymbol{f}\) and \(\mathrm{g}\) are onto but not one-one

117095 The number of bijective functions \(f: Z \rightarrow Z\) such that \(f(x+y)=f^{\prime}(x)+f(y) \forall x, y \in Z\) is

117096 For each \(n \in N\), let \(A_n=\{(n+1) k / k \in N\}\) and \(X\) \(=\bigcup_{n \in N} A_n \cdot A\) mapping \(f: X \rightarrow N\) defined by \(f(x)\) \(=\mathbf{x}, \forall \mathbf{x} \in \mathbf{X}\), is

117093 If \(f: N \rightarrow R\) is defined by \(f(1)=-1\) and \(f(n+1)\) \(=3 \mathrm{f}(\mathrm{n})+\mathbf{2}\) for \(n \geq 1\) then \(f\) is

117094 Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) and \(\mathbf{g}: \mathbf{R} \rightarrow \mathbf{R}\) be the functions defined by
\(f(x)=\frac{x}{1+x^2}, x \in R, g(x)=\frac{x^2}{1+x^2}, x \in I R\)
Then, the correct statement (s) among the following is/are
A : Both \(f, g\) are one-one
B :Both \(f, g\) are onto
C : Both \(f, g\) are not one-one as well as not onto
\(\mathrm{D}: \boldsymbol{f}\) and \(\mathrm{g}\) are onto but not one-one

117095 The number of bijective functions \(f: Z \rightarrow Z\) such that \(f(x+y)=f^{\prime}(x)+f(y) \forall x, y \in Z\) is

117096 For each \(n \in N\), let \(A_n=\{(n+1) k / k \in N\}\) and \(X\) \(=\bigcup_{n \in N} A_n \cdot A\) mapping \(f: X \rightarrow N\) defined by \(f(x)\) \(=\mathbf{x}, \forall \mathbf{x} \in \mathbf{X}\), is

117093 If \(f: N \rightarrow R\) is defined by \(f(1)=-1\) and \(f(n+1)\) \(=3 \mathrm{f}(\mathrm{n})+\mathbf{2}\) for \(n \geq 1\) then \(f\) is

117094 Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) and \(\mathbf{g}: \mathbf{R} \rightarrow \mathbf{R}\) be the functions defined by
\(f(x)=\frac{x}{1+x^2}, x \in R, g(x)=\frac{x^2}{1+x^2}, x \in I R\)
Then, the correct statement (s) among the following is/are
A : Both \(f, g\) are one-one
B :Both \(f, g\) are onto
C : Both \(f, g\) are not one-one as well as not onto
\(\mathrm{D}: \boldsymbol{f}\) and \(\mathrm{g}\) are onto but not one-one

117095 The number of bijective functions \(f: Z \rightarrow Z\) such that \(f(x+y)=f^{\prime}(x)+f(y) \forall x, y \in Z\) is

117096 For each \(n \in N\), let \(A_n=\{(n+1) k / k \in N\}\) and \(X\) \(=\bigcup_{n \in N} A_n \cdot A\) mapping \(f: X \rightarrow N\) defined by \(f(x)\) \(=\mathbf{x}, \forall \mathbf{x} \in \mathbf{X}\), is

117093 If \(f: N \rightarrow R\) is defined by \(f(1)=-1\) and \(f(n+1)\) \(=3 \mathrm{f}(\mathrm{n})+\mathbf{2}\) for \(n \geq 1\) then \(f\) is

117094 Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) and \(\mathbf{g}: \mathbf{R} \rightarrow \mathbf{R}\) be the functions defined by
\(f(x)=\frac{x}{1+x^2}, x \in R, g(x)=\frac{x^2}{1+x^2}, x \in I R\)
Then, the correct statement (s) among the following is/are
A : Both \(f, g\) are one-one
B :Both \(f, g\) are onto
C : Both \(f, g\) are not one-one as well as not onto
\(\mathrm{D}: \boldsymbol{f}\) and \(\mathrm{g}\) are onto but not one-one

117095 The number of bijective functions \(f: Z \rightarrow Z\) such that \(f(x+y)=f^{\prime}(x)+f(y) \forall x, y \in Z\) is

117096 For each \(n \in N\), let \(A_n=\{(n+1) k / k \in N\}\) and \(X\) \(=\bigcup_{n \in N} A_n \cdot A\) mapping \(f: X \rightarrow N\) defined by \(f(x)\) \(=\mathbf{x}, \forall \mathbf{x} \in \mathbf{X}\), is