Question

$f:N\to N$ where $f\left(x\right)=x-{\left(-1\right)}^x$ then $f$ is.

• A. One-one and on to
• B. Many-one and into
• C. One-one and into
• D. Many-one and onto

Answer 1

The correct option is A One-one and on to

Solution-

$f\left(x\right)=x-(-1{)}^x$

$f:N\to N$

$f\left(1\right)=1-(-1{)}^1$

$=2$

$f\left(2\right)=2-(-1{)}^2$

$=1$

$f\left(3\right)=3-(-1{)}^3$

$=4$

$f\left(4\right)=4-(-1{)}^4$

$=3$.

.

.

.

.

It is clearly one-one

because it will not give the same values on

two different $x$ and

it is clearly onto because it covers all

natural number like $2,1,4,3,6,\mathrm{5...}$

$A$ is correct.