Questions: Determine algebraically whether the given function is even, odd, or neither.
f(x)=2/x^(14)
Is the given function even, odd, or neither?
A. Even
B. Odd
C. Neither
Transcript text: Determine algebraically whether the given function is even, odd, or neither.
\[
f(x)=\frac{2}{x^{14}}
\]
Is the given function even, odd, or neither?
A. Even
B. Odd
C. Neither
Solution
Solution Steps
To determine if a function is even, odd, or neither, we check the symmetry properties:
A function f(x) is even if f(−x)=f(x) for all x.
A function f(x) is odd if f(−x)=−f(x) for all x.
For the given function f(x)=x142, we will calculate f(−x) and compare it to f(x).
Step 1: Determine f(−x)
Given the function f(x)=x142, we calculate f(−x):