If f(x)=3x4−5x2+k is an even function, then which of the following describes the value of k (where k is a constant).
A
k is an integer
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B
k is a fraction
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C
k is irrational
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D
k is natural.
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Solution
The correct option is Dk is natural. If f(x)=3x4−5x2+k is an even function f(−x)=3(−x)4−5(−x)2+k=3x4−5x2+k=f(x) which is even ∴ It is not depending on k and it holds the same for any value of k. Therefore, k can be any real number. ∴k can be integer, fraction, irrational or a natural number.