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Let $f= \left \{(2,4), (5,6), (8, -1), (10, -3)\right \}$ and $g = \left \{(2, 5), (7,1), (8,4), (10,13), (11, 5)\right \}$ be two real functions. Then match the following:

a f-g i $\left \{ \left ( 2,\frac{4}{5} \right ),\left ( 8,\frac{-1}{4} \right ),\left ( 10,\frac{-3}{13} \right ) \right \}$

b f+g ii $\left \{ \left ( 2,20 \right ),\left ( 8,-4 \right ),\left ( 10,-39 \right ) \right \}$

c fxg iii $\left \{ \left ( 2,-1 \right ),\left ( 8,-5 \right ),\left ( 10,-16 \right ) \right \}$

d f/g iv $\left \{ \left ( 2,9 \right ),\left ( 8,3 \right ),\left ( 10,10 \right ) \right \}$

Answers (1)

Given data: $f= \left \{(2,4), (5,6), (8, -1), (10, -3)\right \}$ and $g = \left \{(2, 5), (7,1), (8,4), (10,13), (11, 5)\right \}$

$Domain of f(x)$ is \{2,5,8,10\}, Domain of g(x)$ is \{2,7,8,10,11\}$

Now, f-g, f+g, f.g & f/g are defined in the domain $\{2,8,10\}$

$(f-g)2 = f(2) - g(2) = -1$

$(f-g)(8) = -5$

$(f-g)(10) = -16$

Thus, $(f-g) = \left \{(2,-1),(8,-5),(10,16)\right \}$

$(f+g) (2)= f(2) + g(2) = 9$

$(f+g)(8) = 3$

$(f+g)(10) = 10$

Thus, $(f+g) = \left \{(2,9),(8,3),(10,10)\right \}$

$(f.g)(2) = f(2) . g(2) = 20$

$(f.g) (8)= -4$

$(f.g)(10) = -39$

Thus, $(f.g) = \left \{(2,20),(8,-4),(10,-39)\right \}$

$(f/g)(2) = f(2)/g(2) = 4/52(f/g) = f(2)/g(2) = 4/5$

$(f/g)(8) = -1/4$

$(f/g)(10) = -3/13$

Thus, $V = \left \{(2,4/5), (8,(-1/4), (10,-3/13)\right \}$

Thus, the correct matches will be-

$(a)\rightarrow (iii), (b)\rightarrow (iv), (c) \rightarrow (ii) \& (d) \rightarrow (i)$

Posted by

infoexpert21

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