Question

Let $A = \{1$, $2$, $3\}$ and $B = \{2$, $4$, $6$, $8\}$.
Consider the rule $f : A \to B$, $f \left(x\right)=2x\,\forall\,x \in A$. The domain, co-domain and range of $f$ respectively are

• A. $\{1$, $2$, $3\}$, $\{2$, $4$, $6\}$, $\{2$, $4$, $6$, $8\}$
• B. $\{1$, $2$, $3\}$, $\{2$, $4$, $6$, $8\}$, $\{2$, $4$, $6\}$
• C. $\{2$, $4$, $6$, $8\}$, $\{2$, $4$, $6$, $7\}$, $\{1$, $2$, $3\}$
• D. $\{2$, $4$, $6\}$, $\{2$, $4$, $6$, $8\}$, $\{1$, $2$, $3\}$

Answer 1

Answer: (B)

Given, $f(x) = 2x$, $\forall\, x \in A$
Value of function at $x =1$, $f(1)=2(1)=2$
Value of function at $x = 2$, $f(2) = 2(2) = 4$
Value of function at $x = 3$, $f(3) = 2(3) = 6$
Domain of $f= \{1$, $2$, $3\}$
Co-domain of $f= \{2$, $4$, $6$, $8\}$
Range of $f= \{2$, $4$, $6\}$