Question

If $y=f\left(x\right),$ where $f:A\to B$ is a function in $x,$ then which of the following statements is true?

(i) Every element of $A$ needs to have an image.

(ii) $x\in A$ must be related to one and only one value of $y$ of $B.$

• A. Statement (i) is true, but statement (ii) is false.
• B. Statement (ii) is true, but statement (i) is false.
• C. Both statements (i) and (ii) are true.
• D. Neither statement (i) nor statement (ii) is true.

Answer 1

The correct option is C

Both statements (i) and (ii) are true.

A relation $f$ from set $A$ to set $B$ is said to be a function if each element of $A$ has one and only one image in $B.$

Thus, it is necessary for every element of $A$ to have an image in $B.$ It is also necessary that an element of $A$ has a unique image in $B.$
Thus, both the statements are true.