117071
Let \(f\) and \(g\) be periodic functions with the periods \(T_1\) and \(T_2\) respectively. They \(f+g\) is
1 Periodic with period \(\mathrm{T}_1+\mathrm{T}_2\)
2 Non-periodic
3 Periodic with the period \(\mathrm{T}_1\)
4 Periodic when \(T_1=T_2\)
Explanation:
D We have, \(\mathrm{f}\) and \(\mathrm{g}\) be periodic function with periods \(T_1\) and \(T_2\) respectively. \(\mathrm{f}+\mathrm{g}\) is periodic if \(\mathrm{T}_1=\mathrm{T}_2\)
WB JEE-2021
Sets, Relation and Function
117086
If \(f: Z \rightarrow Z\) is defined by \(f(x)=\left\{\begin{array}{ll}\frac{x}{2}, & \text { if } x \text { is even } \\ 0, & \text { if } x \text { is odd }\end{array}\right.\), then \(f\) is
1 onto but not one-to-one
2 one-to-one but not onto
3 one-to-one and onto
4 neither one-to-one nor onto
Explanation:
A \(\mathrm{f}\) is onto and but not one to one as all odd value \(x\) has a 0 assigned in \(f(x)\). Function is onto. as every. element. in \(\mathrm{f}(\mathrm{x})\) is mapped to some element in \(\mathrm{x}\).
117071
Let \(f\) and \(g\) be periodic functions with the periods \(T_1\) and \(T_2\) respectively. They \(f+g\) is
1 Periodic with period \(\mathrm{T}_1+\mathrm{T}_2\)
2 Non-periodic
3 Periodic with the period \(\mathrm{T}_1\)
4 Periodic when \(T_1=T_2\)
Explanation:
D We have, \(\mathrm{f}\) and \(\mathrm{g}\) be periodic function with periods \(T_1\) and \(T_2\) respectively. \(\mathrm{f}+\mathrm{g}\) is periodic if \(\mathrm{T}_1=\mathrm{T}_2\)
WB JEE-2021
Sets, Relation and Function
117086
If \(f: Z \rightarrow Z\) is defined by \(f(x)=\left\{\begin{array}{ll}\frac{x}{2}, & \text { if } x \text { is even } \\ 0, & \text { if } x \text { is odd }\end{array}\right.\), then \(f\) is
1 onto but not one-to-one
2 one-to-one but not onto
3 one-to-one and onto
4 neither one-to-one nor onto
Explanation:
A \(\mathrm{f}\) is onto and but not one to one as all odd value \(x\) has a 0 assigned in \(f(x)\). Function is onto. as every. element. in \(\mathrm{f}(\mathrm{x})\) is mapped to some element in \(\mathrm{x}\).
