Convert to Standard Form: Unfolding f(x) = -(x+1)(x-1)

To solve this problem, we need to convert the given function $f(x) = -(x+1)(x-1)$ from its current product form to standard form.

Let's follow these steps:

• Step 1: Recognize that the expression $(x+1)(x-1)$ is a standard difference of squares formula, expressed as $(a+b)(a-b) = a^2 - b^2$, where $a = x$ and $b = 1$.
• Step 2: According to the formula, $(x+1)(x-1) = x^2 - 1^2 = x^2 - 1$.
• Step 3: Substitute this result back into the function: $f(x) = -(x^2 - 1)$.
• Step 4: Simplify the expression by distributing the negative sign: $-(x^2 - 1) = -x^2 + 1$.

Therefore, the function in its standard form is $f(x) = -x^2 + 1$.

This matches with choice 1: $f(x)=-x^2+1$.