Question

Use the following function rule to find g(y–1). Simplify your answer.
g(z)=z2–3
g(y–1)=

Answer 1

To find \( g(y-1) \) using the function rule \( g(z) = z^2 - 3 \), we will substitute \( z \) with \( y - 1 \).

1. Start with the function definition:
\[
g(z) = z^2 - 3
\]

2. Substitute \( z \) with \( y - 1 \):
\[
g(y-1) = (y - 1)^2 - 3
\]

3. Now, expand \( (y - 1)^2 \):
\[
(y - 1)^2 = y^2 - 2y + 1
\]

4. Substitute this back into the equation:
\[
g(y-1) = (y^2 - 2y + 1) - 3
\]

5. Simplify the expression:
\[
g(y-1) = y^2 - 2y + 1 - 3
\]
\[
g(y-1) = y^2 - 2y - 2
\]

Thus, the simplified answer is:
\[
g(y-1) = y^2 - 2y - 2
\]