Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.
{Use of Tech} $f\left(x\right)=\frac{1}{x^2}$

Verified step by step guidance

1. Step 1: Understand that for a function to have an inverse, it must be one-to-one (bijective). A function is one-to-one if it passes the horizontal line test, meaning no horizontal line intersects the graph of the function more than once.
2. Step 2: Consider the function f(x) = \frac{1}{x^2}. Analyze its behavior: as x approaches 0 from either side, f(x) approaches infinity, and as x approaches positive or negative infinity, f(x) approaches 0.
3. Step 3: Note that f(x) = \frac{1}{x^2} is not one-to-one over its entire domain because for any positive y, there are two x-values (one positive and one negative) that map to y. This violates the horizontal line test.
4. Step 4: To find the largest possible set where f(x) has an inverse, restrict the domain to either x > 0 or x < 0. This restriction ensures that the function is one-to-one, as each y-value corresponds to exactly one x-value.
5. Step 5: Conclude that the largest possible sets of points on which f(x) = \frac{1}{x^2} has an inverse are the intervals (0, ∞) or (-∞, 0). On these intervals, the function is strictly decreasing or increasing, respectively, and thus one-to-one.