Determine whether f(x)=x^2 is one to one.

When I substitute values in for x even when I use negative values x^2 will be positive so is it one to one?

To determine whether the function f(x) = x^2 is one-to-one, we need to examine its behavior with respect to inputs and outputs.

A function is considered one-to-one (or injective) if every distinct input value produces a unique output value. In other words, no two different input values can give the same output value.

In the case of the function f(x) = x^2, we can see that for positive input values, the output values are positive as well. For example, if we substitute x = 2, f(2) = 2^2 = 4, and if we substitute x = 3, f(3) = 3^2 = 9.

The same is true for negative input values. For example, if we substitute x = -2, f(-2) = (-2)^2 = 4, and if we substitute x = -3, f(-3) = (-3)^2 = 9.

From these examples, we can observe that different input values can indeed produce the same output value, which means that the function f(x) = x^2 is not one-to-one.

In general, for a function to be one-to-one, each different input value must correspond to a unique output value. In the case of f(x) = x^2, input values with opposite signs can produce the same output value, resulting in a violation of the one-to-one condition.