Question

if 2f(x) - 3f(1/x) = x^2, determine f(2). What would the steps be to solve this?

Answer 1

You can write two equations one for x=2 one for x=1/2
It will have two variables f(2) and f(1/2)
Solving it will give you f(2) and f(1/2)

Answer 2

I have the answer key and it is saying that f(2) = -7/4

Answer 3

Might be

Answer 4

Alright, i'll try it out! thanks!

Answer 5

If you are stuck let me know and good luck!

Answer 6

Thank you so much!

Answer 7

yes -7/4 is the correct answer

Answer 8

So I would have 1. f(2) and 2. f(1/2) and I would subsitute that into the function two times?

Answer 9

Not really.
First set x=2 and write up an equation
Than set x=1/2 and do the same.

Answer 10

After I set x = 2, I get 4 - 3/2 = 4
which doesn't do much for me

Answer 11

when x=2
2f(2)-3f(1/2)=4

Answer 12

You do not know what the function f does

Answer 13

So what would I do after that when I am left with 2f(2)-3f(1/2)=4

Answer 14

write up the same when x=1/2

Answer 15

then?

Answer 16

then you have two equations with two unknown variables and I guess you already learnt how to solve that

Answer 17

So I can either use the subsitution or elimination method?

Answer 18

I got it!

Answer 19

Very good