Solve Quadratic Function: Finding x When f(x) = x² Equals 81

To solve this problem, we'll follow these steps:

• Step 1: Set up the equation $x^2 = 81$.
• Step 2: Solve for $x$ by taking the square root of both sides.
• Step 3: Confirm that the solutions are integers provided in the choices.

Now, let's work through each step:
Step 1: The problem gives us the function $f(x) = x^2$ and asks us to find values of $x$ such that $f(x) = 81$
Step 2: Solving $x^2 = 81$, we take the square root of both sides to get $x = \pm \sqrt{81}$.
Step 3: Compute $\sqrt{81} = 9$, which gives us $x = 9$ or $x = -9$. Therefore, the solutions are $x = 9$ and $x = -9$.

Considering the given choices, we can identify that $f(-9) = 81$, which corresponds to choice 1 in the problem.

Therefore, the solution to the problem is $\boldsymbol{f(-9)}$.