If 2F (x) - f (1 / 3) = 3x + 2, find the analytic expression of F (x)

If 2F (x) - f (1 / 3) = 3x + 2, find the analytic expression of F (x)

Because 2F (x) - f (1 / 3) = 3x + 2, if x = 1 / 3, then 2F (1 / 3) - f (1 / 3) = 3
So f (1 / 3) = 3, which is substituted into the equation
2f(x)=3x+5

Given that f (x) satisfies if 2F (x) + F (1 / x) = 3x (x > 0), find f (x)

2f(x)+f(1/x)=3x (1)
Let a = 1 / x, x = 1 / A
So 2F (1 / a) + F (a) = 3 / A
So 2F (1 / x) + F (x) = 3 / X (2)
(1)×2-(2)
3f(x)=6x-3/x=3(2x²-1)/x
f(x)=(2x²-1)/x,x>0

If 2F (x) + F (- x) = 3x + 1, then find the analytic expression of F (x)

F (x) is a linear function
So let f (x) = ax + B
There are 2F (x) + F (- x) = 3x + 1
Then 2aX + 2B ax + B = 3x + 1
That is ax + 3B = 3x + 1
Then a = 3, B = 1 / 3
So f (x) = 3x + 1 / 3

Given that f (x) + 2F (1 / x) = 3x, find the analytic expression of F (x)

f(x)+2f(1/x)=3x (1)
Let x = 1 / X
f(1/x)+2f(x)=3/x (2)
（2）×2-(1)
3f(x)=6/x-3x
f(x)=2/x-x