Question

\(f(x)\) is real valued function such that \(2 f(x)+3 f(-x)=15-4 x\) for all \(x \in R\). Then \(f(2)=\)
(A) \(-15\)
(B) 22
(C) 11
(D) 0

Answer 1

Ans: (C)
Hint : \(2 f(x)+3 f(-x)=15-4 x \quad \ldots .\) (1)
Replace \(x\) by \(-x\)
$$
2 f(-x)+3 f(x)=15+4 x
$$
After solving (1) and (2), we get
$$
\begin{aligned}
&f(x)=4 x+3 \\
&\therefore f(2)=8+3=11
\end{aligned}
$$

Answer 2

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Answer 3

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