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Question: If f(x) = \(\left| \begin{matrix} 2^{- x} & e^{x\log_{e}2} & x^{2} \\ 2^{- 3x} & e^{3x\log_{e}2} & x...

If f(x) = ∣2−xexlog⁡e2x22−3xe3xlog⁡e2x42−5xe5xlog⁡e21∣\left| \begin{matrix} 2^{- x} & e^{x\log_{e}2} & x^{2} \\ 2^{- 3x} & e^{3x\log_{e}2} & x^{4} \\ 2^{- 5x} & e^{5x\log_{e}2} & 1 \end{matrix} \right| Then

A

f(x) + f(–x) = 0

B

f(x) – f(–x) = 0

C

f(x) + f(–x) = 2

D

None of these

Answer

f(x) + f(–x) = 0

Explanation

Solution

f(x) = ∣2−x2xx22−3x23xx42−5x25x1∣\left| \begin{matrix} 2^{- x} & 2^{x} & x^{2} \\ 2^{- 3x} & 2^{3x} & x^{4} \\ 2^{- 5x} & 2^{5x} & 1 \end{matrix} \right| f(–x) = ∣2x2−xx223x2−3xx425x2−5x1∣\left| \begin{matrix} 2^{x} & 2^{- x} & x^{2} \\ 2^{3x} & 2^{- 3x} & x^{4} \\ 2^{5x} & 2^{- 5x} & 1 \end{matrix} \right| = – f(x)