Question

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Answer 1

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Given:-

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=> f(x) + 2f(1/x) =3x-----(1)

Now , we can also say ,

=> f(y) + 2f(1/y) =3y-----(2)

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Let y = 1/x

=> f(1/x) + 2f(x) = 3/x ----(3)

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Now ... lets do equation(3)×2

=> 2f(1/x) + 4f(x) = 6/x ---(4)

Now, equation (4) -(1)

=> 4f(x) - f(x) = (6/x) -3x

=> 3×f(x) = 3{(2/x)- x}

=> f(x) = (2/x) - x

=> f(x) =( 2 - x² )/x

to find the elements present in it,

we have ro make function f(x) =0.

so

=> f(x) = (2-x²)/x =0

=> f(x) = 2 - x² = 0 (since , x≠0)

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Note :-

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here , f(x) = 2-x² = f(-x)

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=> 2 - x² = 0

=> (x+ √2)(√2 -x)=0

So...

=> x = ±√2

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Hence, it contains exactly two elements.

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Hope (3) is your required answer

Proud to help you.

Answer 2

Answer:

x = +√2

Step-by-step explanation: