Question

Let $A=\{x:-1\le x\le 1\}$ and $f:A\to A$ is a function defined by $f\left(x\right)=x|x|$, then f is

• A. a bijection
• B. injection but not surjection
• C. Surjection but not injection
• D. neither injection nor surjection

Answer 1

The correct option is A a bijection

The graph of $f\left(x\right)=x|x|$shows that it is a bijective function.

Since, distinct elements of the domain set mapping to the distinct elements in the codomain set.
So, the function is one-one.
And also every element of co-domain set has a pre-image element in domain, so the function is onto function also.
Therefore, the given function is a bijective function.