Checkpoint: Evaluating Functions Solution

Evaluate $j (x - 1)$ for $j (x) = x^{3} - 2 x .$

$j (x - 1) = x^{3} - 2 x j (x - 1) = {(x - 1)}^{3} - 2 (x - 1) j (x - 1) = (x - 1) (x^{2} - 2 x + 1) - 2 x + 2 j (x - 1) = x^{3} - 2 x^{2} + x - x^{2} + 2 x - 1 - 2 x + 2 j (x - 1) = x^{3} - 3 x^{2} + x + 1$

Note

Q: With what will x be replaced in the function?

A: x – 1

Show your work to avoid errors. You are familiar with substitution and need to work carefully to ensure the correct answers.