If f = {(4, 5), (5, 6), (6, -4) and g = {(4, -4), (6, 5),(8, 5)} then find
$A) f + g B) f - g C) 2 f + 4 g D) f + 4 E) f g F) f / g G) | f | H) \sqrt{f} I) f^{2} G) f^{3}$

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Solution

$f = {(4, 5), (5, 6), (6, - 4)}$ and $g = {(4, - 4), (6, 5), (8, 5)}$
Binary operations are done on common domain.
$A) f + g = {(4, 1)}$
$B) f - g = {(4, 9)}$
$C) 2 f + 4 g = {(4, - 6)}$
$D) f + 4 = {(4, 9), (5, 10), (6, 0)}$
$E) f g = {(4, - 20)}$
$F) f / g = {(4, \frac{5}{- 4})}$
$G) | f | = {(4, 5), (5, 6) (6, 4)}$
$H) \sqrt{f} = {(4, \sqrt{5}), (5, \sqrt{6})}$
$I) f^{2} = {(4, 25), (5, 36), (6, 16)}$
$J) f^{3} = {(4, 125), (5, 216), (6, - 64)}$
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