When using the order of operations to transform f(x)=x^2 + 12 to 2f(x-3) what needs to be completed first

Question

Square the expression (x-3)
Multiply (x-3) by 2
Add12 to (x-3)

Answer 1

To transform \( f(x) = x^2 + 12 \) into \( 2f(x-3) \), let's break down the steps according to the order of operations.

1. Function Substitution: You need to evaluate \( f(x - 3) \). This involves substituting \( x - 3 \) into the function \( f(x) \).

   \[ f(x - 3) = (x - 3)^2 + 12 \]

   Here, you must first square the expression \( (x - 3) \).

2. Calculate \( f(x - 3) \): Now, after squaring, the expression will look like this:

   \[ f(x - 3) = (x - 3)^2 + 12 \]

3. Multiply by 2: After calculating \( f(x - 3) \), the next step is to multiply the entire expression by 2:

   \[ 2f(x - 3) = 2 \left( (x - 3)^2 + 12 \right) \]

So, the correct order of operations is:

1. Square the expression \( (x - 3) \) first.
2. Then, add 12 to the squared result.
3. Finally, multiply the whole expression by 2.

In summary, the first step is to square the expression \( (x - 3) \).