Let f be a function satisfying the functional equation fx - 2f 2x-1-x-2 - 3x- x - 2- then- the value of f7 is

Replace x →2x+1/x 2 f ( 2x+1/x 2 ) + 2f(x) =3 ( 2x+1/x 2 ) (1) Given f(x) + 2 f ( 2x +1/x 2 )= 3x (2) Solving (1) amp; (2) f(x) = x^2 +6x+2/x 2 f(7) = 44 ...

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Standard XIII

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Question

Let f be a function satisfying the functional equation $f (x) + 2 f (\frac{2 x + 1}{x - 2}) = 3 x, x \neq 2$ ; then, the value of f(7) is

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Solution

The correct option is D -1
Replace $x \to \frac{2 x + 1}{x - 2}$
$f (\frac{2 x + 1}{x - 2}) + 2 f (x) = 3 (\frac{2 x + 1}{x - 2}) - (1)$
Given $f (x) + 2 f (\frac{2 x + 1}{x - 2}) = 3 x - (2)$
Solving (1) & (2)
$f (x) = \frac{- x^{2} + 6 x + 2}{x - 2}$
$f (7) = \frac{44 - 49}{5} = - 1$

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Let f be a function satisfying the functional equation f(x)+2f(2x+1x−2)=3x,x≠2; then, the value of f(7) is

The correct option is D -1Replace x→2x+1x−2 f(2x+1x−2)+2f(x)=3(2x+1x−2)−(1) Given f(x)+2f(2x+1x−2)=3x−(2) Solving (1) & (2) f(x)=−x2+6x+2x−2 f(7)=44−495=−1

Let f be a function satisfying the functional equation $f (x) + 2 f (\frac{2 x + 1}{x - 2}) = 3 x, x \neq 2$ ; then, the value of f(7) is

The correct option is D -1
Replace $x \to \frac{2 x + 1}{x - 2}$
$f (\frac{2 x + 1}{x - 2}) + 2 f (x) = 3 (\frac{2 x + 1}{x - 2}) - (1)$
Given $f (x) + 2 f (\frac{2 x + 1}{x - 2}) = 3 x - (2)$
Solving (1) & (2)
$f (x) = \frac{- x^{2} + 6 x + 2}{x - 2}$
$f (7) = \frac{44 - 49}{5} = - 1$