Question

If 2f(x)+3f(1/x)=2x+3,find f(x)

Answer 1

Answer:

f(x) = ( -4x²+3x+6)/5x

Step-by-step explanation:

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

setting x=1/x then

f (1/x)=f(1/1/x)= f(x) and f(x)=f(1/x)

so(1) becomes

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

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

Multiplying (1) by 2  and (2) by 3 we get

4 f(x)+6 f( 1/x )=4x+6--------------(3)

9 f(x)+6 f( 1/x )= ( 6+9x )/x--------------(4)

Now subtracting (3) from (4)

5 f(x) =(6+9x)/x-4x-6=(6+9x-4x²-6x)/x

5 f(x) = ( -4x²+3x+6)/x

f(x) = ( -4x²+3x+6)/5x

Answer 2

Answer:

Step-by-step explanation: