Question

Use the following function rule to find f(2x). Simplify your answer.
f(v)=v2+2v
f(2x)=

Answer 1

To find \( f(2x) \) using the given function rule \( f(v) = v^2 + 2v \), we will replace \( v \) with \( 2x \) in the function.

1. Start with the function:
\[
f(v) = v^2 + 2v
\]

2. Replace \( v \) with \( 2x \):
\[
f(2x) = (2x)^2 + 2(2x)
\]

3. Now calculate \( (2x)^2 \):
\[
(2x)^2 = 4x^2
\]

4. Calculate \( 2(2x) \):
\[
2(2x) = 4x
\]

5. Combine these results:
\[
f(2x) = 4x^2 + 4x
\]

Thus, the simplified expression for \( f(2x) \) is:
\[
\boxed{4x^2 + 4x}
\]