If $$2f(x)+3f(-x)=x^3+x+5$$, find the value of $$f(-1) $$

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Uniteasy Admin · Accepted Answer

Substituting $$x=1$$ to the given equation gives
$$2f(1)+3f(-1)=1^3+1+5$$
then,
$$2f(1)+3f(-1)=7$$n
Substituting $$x=-1$$ to the given equation gives
$$2f(-1)+3f(1)=(-1)^3-1+5$$
then,
$$2f(-1)+3f(1)=3$$n
Solve the system of equations in terms of $$f(1)$$ and $$f(-1)$$
$$\begin{cases} 2f(1)+3f(-1)=7 \ 2f(-1)+3f(1)=3 \end{cases}$$
then,
$$f(-1) = 3$$

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