Question

Determine whether the function f is even, odd, or neither.

x^-6

Answer 1

Usually if the exponent of a simple power function is even, the function is even, which means the graph looks the same on both sides of the y-axis

Answer 2

f(x) is even if f(-x) = f(x)

f(x) is odd if f(-x) = -f(x)

Hence if

\[f(x)=\frac{ 1 }{ x ^{6} }\] then first find f(-x). Thus

\[f(-x)=\frac{ 1 }{ (-x)^{6} }\]
\[=\frac{ 1 }{ x ^{6} }\]

Thus f(-x) = f(x)

∴ f(x) is an even function.

Do you understand?