A) even integer
B) odd integer
C) any integer
D) \[f(x)\] even is not possible
Correct Answer: B
Solution :
Given, \[f(x)=\sqrt[n]{{{x}^{m}}},\,\,n\in N\]is an even function. where \[m\in I\]. \[\Rightarrow \] \[f(x)=f(-x)\Rightarrow \sqrt[n]{{{x}^{m}}}=\sqrt[n]{{{(-x)}^{m}}}\] \[\Rightarrow \] \[{{x}^{m}}={{(-x)}^{m}}\] \[\Rightarrow \] \[m\]is an even integer. \[\therefore \] \[m=2,\,\,k\in I\]
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