Question

determine whether the following function is one-to-one.

(f(x) = \frac{2}{x})

• the function is one-to-one.
• the function is not one-to-one.

Explanation:

Step 1: Assume equal outputs

Assume \(f(a) = f(b)\) for any \(a, b\) in the domain.

$$\frac{2}{a} = \frac{2}{b}$$

Step 2: Solve for variables

Cross-multiply to solve for the variables.

$$2a = 2b$$

Step 3: Simplify the equation

Divide both sides by 2 to simplify.

$$a = b$$

Answer:

The function is one-to-one.