If 2 f ( x ) + 3 f ( 1 x ) = 4...

John Landry

John Landry

Answered

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

Expert

2022-07-20Added 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

Expert

2022-07-21Added 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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?