What is f(x) if f(x)-2f(-x)=3x-1

As we can notice, the given expression f(x)-2f(-x)=3x-1 is
a linear
function.

 f(x)=ax+b.

We'll
substitute "x" by "-x" and we'll rewrite the above
expression.

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

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

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

We'll consider f(x) and f(-x) as
unknowns.

We'll multiply the expression (1) by the value
"+2" and after that we'll add the expression (1) to the expression
(2).

2f(-x)-4f(x)-2f(-x)+f(x)=-6x-2+3x-1

-3f(x)=-3x-3

We'll
divide the expression by
"-3"

f(x)=x+1

where
a=1 and b=1