A) neither one-one nor onto
B) onto but not one-one
C) both one-one and onto
D) one-one but not onto
Correct Answer: B
Solution :
For f(g(n)) \[at,\text{ }n=1\] \[g\left( n \right)=1-{{\left( -1 \right)}^{1}}\] \[=\text{ }1-\left( -1 \right)=2\] \[f\left( 2 \right)=\frac{2}{2}=1\] at, \[n=2\] \[g\left( n \right)=2-{{\left( -1 \right)}^{2}}\] \[=\text{ }2-\left( 1 \right)=1\] \[f\left( 1 \right)=0\] at, \[n\,\,=\,\,3\] \[g\left( n \right)=3-{{\left( -1 \right)}^{3}}\] \[=\text{ }3-\left( -1 \right)=4\] \[f\left( 4 \right)=2\] at, \[n=4\] \[g\left( n \right)=4-{{\left( -1 \right)}^{4}}\] \[=4-\left( 1 \right)=3\] \[f\left( 3 \right)=1\] many one onto or onto but not one-oneYou need to login to perform this action.
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