Given $f(x)=-5 x^{8}+2|x|$, answer the following: Part: 0 / 3 Part 1 of 3 (a) Find $f(-x)$. \[ f(-x)=\square \]

Step 1 ：Given the function \(f(x) = -5x^8 + 2|x|\)

Step 2 ：We are asked to find \(f(-x)\)

Step 3 ：Substitute \(-x\) for \(x\) in the function, we get \(f(-x) = -5(-x)^8 + 2|-x|\)

Step 4 ：Since the absolute value function \(|x|\) is even, meaning it is symmetric about the y-axis, we have \(|-x| = |x|\)

Step 5 ：Also, any even power of \(-x\) is the same as the same power of \(x\), so \((-x)^8 = x^8\)

Step 6 ：Therefore, \(f(-x) = -5x^8 + 2|x|\)

Step 7 ：Final Answer: \(f(-x) = \boxed{-5x^8 + 2|x|}\)