Question

if 3f(x)+4f(1/x)=1/x-3 for all non zero x then f(x)=​

Answer 1

Answer:

First of all the question should be,

Prove that

f(x³)=[f(x)]³-3f(1/x)

So,

First considering Right hand side,

=[f(x)]³-3f(1/x)

=(x- 1/x )³ -3 (1/x - x)

=(x³ - (1/x)³)  - 3(x × (1/x) (x- 1/x)) -3 (1/x - x)

=(x³ - (1/x)³)  -3 (x- 1/x)   +3 ( x - 1/x)

=x³ - (1/x)³

Now, considering Left hand side.

f(x³)=x³ - (1/x)³

So,

We conclude that LHS= RHS

Hence proved

Answer 2

Explanation:

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