Question

Is 5/ x^2 a one- to - one function. How?

Answer 1

[AI-generated answer — Bot GPT 3.5]

The function 5/x^2 is not a one-to-one function. A one-to-one function is a function where each element of the range is paired with exactly one element of the domain.

In the function 5/x^2, for example, if we have x = 2 and x = -2, the values of the function would be the same since (-2)^2 = 2^2 = 4, and 5/4 is the same as 5/(-4) = -5/4. This means that different inputs can yield the same output, violating the one-to-one requirement. Therefore, 5/x^2 is not a one-to-one function.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine if a given function is one-to-one, we need to check if every input (x-value) corresponds to a unique output (y-value). In this case, the function is f(x) = 5/x^2.

First, let's assume that f(x₁) = f(x₂), where x₁ and x₂ are different values. This means that 5/x₁^2 = 5/x₂^2.

To check if the assumption is correct, we can cross-multiply and solve for x₁ and x₂:

5/x₁^2 = 5/x₂^2
5*x₂^2 = 5*x₁^2
x₂^2 = x₁^2
√(x₂^2) = √(x₁^2)
|x₂| = |x₁|

From this equation, we can see that x₂ is equal to either x₁ or -x₁. Therefore, the function 5/x^2 is NOT one-to-one because for every x value, there is another x value that produces the same output.