Question

A function A(x) is defined at follows:
For x > 0, A(x) = x^3 - x^2 + x
For x < 0, A(x) = -x^3 + x^2 - x
What is the value of A(-3)

Answer 1

To find \( A(-3) \), we need to use the definition of the function \( A(x) \) that applies for \( x < 0 \).

Since \( -3 < 0 \), we use the equation for \( A(x) \) when \( x < 0 \):
\[
A(x) = -x^3 + x^2 - x
\]

Now, we substitute \( x = -3 \) into this equation:
\[
A(-3) = -(-3)^3 + (-3)^2 - (-3)
\]

Calculating each term separately:
1. \( -(-3)^3 = -(-27) = 27 \)
2. \( (-3)^2 = 9 \)
3. \( -(-3) = 3 \)

Now, combine these results:
\[
A(-3) = 27 + 9 + 3
\]

Adding these values together:
\[
27 + 9 = 36
\]
\[
36 + 3 = 39
\]

Thus, the value of \( A(-3) \) is
\[
\boxed{39}
\]