Question

If $f=\left\{\left(4,5\right),\left(5,6\right),\left(6,-4\right)\right\}$ and $g=\left\{\left(4,-4\right),\left(6,5\right),\left(8,5\right)\right\}$ then find
1) $f+g$
2) $f-g$
3) $2f+4g$

Answer 1

Consider the given function

$f=\{(4,5),(5,6),(6,-4)$ ..……(1)

$g=\{(4,-4),(6,5),(8,5)\}$ ……..(2)

Now,

1) $f+g=\left\{\right(4+4,5-4),(5+6,6+5),(6+8,-4+5\left)\right\}=\{(8,1),(11,11),(14,1)\}$

2) $f-g=\left\{\right(4-4,5+4),(5-6,6-5),(6-8,-4-5\left)\right\}=\{(0,9),(-1,1),(-2,-9)\}$

3)$2f+4g=\left\{\right(8,10),(10,12),(12,-8\left)\right\}+\left\{\right(16,-16),(24,20),(32,20\left)\right\}=\left\{\right(8+16,10-16),(10+24,12+20),(12+32,-8+20\left)\right\}=\{(24,-6),(34,32),(44,16)\}$