Question

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

Collected in the board: Function

Steven Zheng posted 2 weeks ago

Answer

Substituting x=1 to the given equation gives

2f(1)+3f(-1)=1^3+1+5

then,

2f(1)+3f(-1)=7
(1)

Substituting x=-1 to the given equation gives

2f(-1)+3f(1)=(-1)^3-1+5

then,

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

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

Steven Zheng posted 2 weeks ago

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