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

Answer

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Answer

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

Steps

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: $f(-x) = \boxed{-5x^8 + 2|x|}$