For any non-zero real number x, let $$f(x) + 2f \left(\cfrac{1}{x}\right) = 3x$$. Then, the sum of all possibl

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For any non-zero real number x, let $$f(x) + 2f \left(\cfrac{1}{x}\right) = 3x$$. Then, the sum of all possible values of x for which $$f(x) = 3$$, is

Accepted Answer

-3. We are given, f ( x ) + 2 f ( 1 x ) = 3 x f(x) + 2f \left(\cfrac{1}{x}\right) = 3x f ( x ) + 2 f ( x 1 ​ ) = 3 x Substituting 1 x f o r x \frac{1}{x}\ for\ x x 1 ​ f or x f ( 1 x ) + 2 f ( x ) = 3 x f\left(\dfrac{1}{x}\right)+2f\left(x\right)=\dfrac{3}{x} f ( x 1 ​ ) + 2 f ( x ) = x 3 ​ Multiplying

For any non-zero real number x, let $f(x) + 2f \left(\cfrac{1}{x}\right) = 3x$ . Then, the sum of all possible values of x for which $f(x) = 3$ , is

For any non-zero real number x, let $f(x) + 2f \left(\cfrac{1}{x}\right) = 3x$ . Then, the sum of all possible values of x for which $f(x) = 3$ , is

For any non-zero real number x, let f(x)+2f(1x)=3xf(x) + 2f \left(\cfrac{1}{x}\right) = 3xf(x)+2f(x1​)=3x. Then, the sum of all possible values of x for which f(x)=3f(x) = 3f(x)=3, is

For any non-zero real number x, let f(x)+2f(1x)=3xf(x) + 2f \left(\cfrac{1}{x}\right) = 3xf(x)+2f(x1​)=3x. Then, the sum of all possible values of x for which f(x)=3f(x) = 3f(x)=3, is

For any non-zero real number x, let $f(x) + 2f \left(\cfrac{1}{x}\right) = 3x$ . Then, the sum of all possible values of x for which $f(x) = 3$ , is

For any non-zero real number x, let $f(x) + 2f \left(\cfrac{1}{x}\right) = 3x$ . Then, the sum of all possible values of x for which $f(x) = 3$ , is