Question

Which among the following functions are invertible?

• A. $f:Z\to Z$ defined by $f\left(x\right)=|x|$
• B. $f:Z\to Z$ defined by $f\left(x\right)=x+2$
• C. $f:Z\to Z$ defined by $f\left(x\right)=x^3$
• D. $f:Z\to Z$ defined by $f\left(x\right)=2x$

Answer 1

The correct option is B $f:Z\to Z$ defined by $f\left(x\right)=x+2$

$f:Z\to Z,f\left(x\right)=x+2$ is one one and onto function. Hence $f\left(x\right)$ is invertible.

$f:Z\to Z,f\left(x\right)=x^3$ is one-one
And the range $\ne Z$. Hence it is not onto function, so not invertible.

$f:Z\to Z$ defined by $f\left(x\right)=2x$ is one one but has only even integers in the range, hence not onto, so not invertible.

$f:Z\to Z$ defined by $f\left(x\right)=|x|$ is many one function. So not invertible.