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Definition of Functions

If f2x+3y,2...

Question

If $f (2 x + 3 y, 2 x - 7 y) = 20 x$ ,then $f (x, y)$ equal to

A

7 x - 3 y

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B

7 x + 3 y

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C

3 x - 7 y

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D

x - y

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Solution

The correct option is C $7 x + 3 y$
In $f (2 x + 3 y, 2 x - 7 y) = 20 x$
Let $2 x + 3 y = X$ ...(1)
and $2 x - 7 y = Y$ ...(2)
Multiplying (1) by $7$ and (2) by $(3)$ we get
$14 x + 21 y = 7 X$ and $6 x - 21 y = 3 Y$
Adding them
$20 x = 7 X + 3 Y$
Hence
$f (X, Y) = 7 X + 3 Y$
or $f (x, y) = 7 x + 3 y$

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