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Question

If 5f(x)+3f(1x) = x+2 and y = xf(x), then (dydx)x=1 is equal to.


A

14

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B

7/8

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C

1

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D

2

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Solution

The correct option is B

7/8


5f(x)+3f(1x) = x + 2

Replacing x by 1x

5f(1x)+3f(x) = 1x+2

From Eq. (i),

25f(x)+15f(1x) = 5x+10

and from Eq. (ii),

9f(x)+15f(1x) = 3x+6

Substracting Eq.(iv) from (iii), we get

16f(x) = 5x3x+4

xf(x) = 5x23+4x16 = 4

dydx = 10x+416

dydxx=1 = 10+416 = 78


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