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Question 1670 :
For any non-zero real number $x$ , let $f (x) + 2 f (\frac{1}{x}) = 3 x$ . Then, the sum of all possible values of $x$ for which $f (x) = 3$ , is

A.
2
B.
-3
C.
-2
D.
3

Video Explanation

Explanatory Answer

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

Put $x = 1 / x$ ,

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

Solving (1) & (2),
(1) $\Rightarrow$

(1) \Rightarrow 2 \times (2) \Rightarrow f (x) + 2 f (1 x) = 3 x 2 f (1 x) + 4 f (x) = 6 x

Subtracting, we get

3 f (x) = 6 x - 3 x

So,

f (x) = 2 x - x

Now,

f (x) = 3 implies, 2 x - x = 3 x 2 + 3 x - 2 = 0

Sum of the roots $= - b / a$
Answer $= - 3$

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

Hence, the answer is '-3'

The question is "For any non-zero real number <mi>x</mi></math>">x, let <mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mi>f</mi><mrow><mo>(</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>)</mo></mrow><mo>=</mo><mn>3</mn><mi>x</mi></math>">f(x)+2f(1/x)=3x. Then, the sum of all possible values of <mi>x</mi></math>">x for which <mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mn>3</mn></math>">f(x)=3, is"

Previous Year Papers

Question 1670 :
For any non-zero real number $x$ , let $f (x) + 2 f (\frac{1}{x}) = 3 x$ . Then, the sum of all possible values of $x$ for which $f (x) = 3$ , is

Video Explanation

Explanatory Answer

Hence, the answer is '-3'

The answer is "<p>-3</p>"

Choice B is the correct answer.

Previous Year Papers

Question 1670 : For any non-zero real number x, let f(x)+2f(1/x)=3x. Then, the sum of all possible values of x for which f(x)=3, is

Video Explanation

Explanatory Answer

Hence, the answer is '-3'

The answer is "<p>-3</p>"

Choice B is the correct answer.

Question 1670 :
For any non-zero real number $x$ , let $f (x) + 2 f (\frac{1}{x}) = 3 x$ . Then, the sum of all possible values of $x$ for which $f (x) = 3$ , is