Question
Given the function \( p \) described by \( p(x)=x^{3}-x \), find \( p(-3) \) \( p(-3)=\square \)
Ask by Weston Bryant. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( p(-3) = -24 \)
Solution
1. Substitute \( x = -3 \) into the function:
\[
p(-3) = (-3)^3 - (-3)
\]
2. Calculate \( (-3)^3 \):
\[
(-3)^3 = -27
\]
3. Compute \( -(-3) \):
\[
-(-3) = 3
\]
4. Combine the results:
\[
p(-3) = -27 + 3 = -24
\]
Thus, \( p(-3) = -24 \).
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Bonus Knowledge
To find \( p(-3) \), you simply substitute \(-3\) for \(x\) in the function \( p(x) = x^3 - x \). So, \[ p(-3) = (-3)^3 - (-3) \] Calculating \((-3)^3\): \[ (-3)^3 = -27 \] Now substituting back: \[ p(-3) = -27 - (-3) = -27 + 3 = -24 \] Thus, \[ p(-3) = -24. \]