If 2f(x)+3f((1)/(x))=(4x^2+6)/(x) and f^(−1)(x)=1 then find the value of x. My Attempt: 2f(x)+3f((1)/(x))=(4x^2+6)/(x) 2f(x)+3f((1)/(x))=4x+6/x At this point, I couldn't get other idea except comparing the corresponding terms. please provide any other method...

John Landry

John Landry

Answered question

2022-07-19

If 2 f ( x ) + 3 f ( 1 x ) = 4 x 2 + 6 x and f 1 ( x ) = 1 then find the value of x
If 2 f ( x ) + 3 f ( 1 x ) = 4 x 2 + 6 x and f 1 ( x ) = 1 then find the value of x
My Attempt:
2 f ( x ) + 3 f ( 1 x ) = 4 x 2 + 6 x
2 f ( x ) + 3 f ( 1 x ) = 4 x + 6 x
At this point, I couldn't get other idea except comparing the corresponding terms. please provide any other method...

Answer & Explanation

dasse9

dasse9

Beginner2022-07-20Added 12 answers

We are trying to find the following:
f 1 ( x ) = 1 x = f ( 1 )
Plugging x = 1 into the original functional equation...
2 f ( 1 ) + 3 f ( 1 ) = 4 + 6 1
5 f ( 1 ) = 10 x = f ( 1 ) = 2
Brenton Dixon

Brenton Dixon

Beginner2022-07-21Added 5 answers

You can solve the following system.
2 f ( x ) + 3 f ( 1 x ) = 4 x 2 + 6 x and 2 f ( 1 x ) + 3 f ( x ) = 4 x 2 + 6 1 x
which gives f ( x ) = 2 x

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