If `f(x)=x^m n ,n in N ,` is an even function, then `m` is even integer (b) odd integer any integer (d) `f(x)-e v e ni snotpos s i b l e`

Options

A. even integer
B. odd integer
C. any integer
D. `f(x)`-even is not possible

Answer

A

Explanation

Given `f(x)=sqrt(n)(x^(m)),n in N,` in an even function where `m in I`. So,
`f(x)=f(-x)`
`or root(n)(x^(m))=root(n)((-x)^(m))`
` or x^(m)=(-x)^(m)`
i.e., m is an integer
` or m=2k, k in I`