Answer the following questions regarding the idea of an onto function.

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Answer the following questions regarding the idea of an onto function. (i) State the definition of a surjective (onto) function. (ii) Let

A=\{1,2,3\}

and

B=\{a,b,c\}

. A function

f:A\to B

is given by

f(1)=a,\;f(2)=b,\;f(3)=b

. Determine whether

f

is onto. Give a clear reason for your answer. (iii) By changing at most one value of

f

, construct a new function

\tilde f:A\to B

that is onto. Write the complete definition of

\tilde f

and justify that it is surjective.