Question

Determine algebraically whether the function is even, odd, or neither even nor odd.
f(x)= -3x^4 - 2x - 5
a. Neither
b. Even
c. Odd

Answer 1

$Given \: f(x) = -3x^{4} - 2x - 5\: ---(1)$

$i ) f(-x) = -3(-x)^{4} - 2(-x) - 5 \\= -3x^{4} + 2x - 5 \neq f(x) , \\\pink {(The \: function \:is \:not \:even)}$

$ii ) -f(x) = -(-3x^{4} -2x - 5 ) \\= 3x^{4} + 2x +5$

$f(-x) \neq -f(x) ,\\\pink { ( The \: function \:is \:not \:odd )}$

$Therefore .,\\ i )f(-x) \neq f(x) \:and \\ii ) f(-x) \neq -f(x) , \\\pink {( the \: function \:is \: neither \:even \:nor \:odd )}$

$Option \: \green { (a) } \:is \: correct.$

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