**Question:**

Let $A=\{2,3,5,7\}$ and $B=\{3,5,9,13,15\} .$ Let $f=\{(x, y): x \in A, y \in B$ and $y=$2 x-1\}$

Write f in roster form. Show that f is a function from A to B. Find the domain and range of f.

**Solution:**

Given: A = {2, 3, 5, 7} and B = {3, 5, 9, 13, 15}

$f=\{(x, y): x \in A, y \in B$ and $y=2 x-1\}$

For $x=2$

$y=2 x-1$

$y=2(2)-1$

$y=3 \in B$

For $x=3$

$y=2 x-1$

$y=2(3)-1$

$y=5 \in B$

For $x=5$

$y=2 x-1$

$y=2(5)-1$

$y=9 \in B$

For $x=7$

$y=2 x-1$

$y=2(7)-1$

$\mathrm{y}=13 \in \mathrm{B}$

$\therefore f=\{(2,3),(3,5),(5,9),(7,13)\}$

Now, we have to show that f is a function from A to B

Function:

(i) all elements of the first set are associated with the elements of the second set.

(ii) An element of the first set has a unique image in the second set.

$f=\{(2,3),(3,5),(5,9),(7,13)\}$

Here, (i) all elements of set A are associated with an element in set B.

(ii) an element of set $\mathrm{A}$ is associated with a unique element in set $\mathrm{B}$.

∴ f is a function.

Dom (f) = 2, 3, 5, 7

Range (f) = 3, 5, 9, 13