Chapter 1.5, Problem 1PT

A function f is one-to-one means:

1. a) if x₁ = x₂, then f(x₁) = f(x₂)
2. b) if x₁ ≠ x₂, then f(x₁) = f(x₂)
3. c) if x₁ ≠ x₂, then f(x₁) = f (x₂)
4. d) if f(x₁) ≠ f(x₂), then x₁ ≠ x₂

To determine

The correct option so that the statement “A function f is one-to-one means $\_\_\_\_\_\_\_$.” is complete.

Answer to Problem 1PT

The correct option is $\underset{\_}{c}$.

Explanation of Solution

Result used:

“A function f is one-to-one means that for all $x_1,x_2$ in the domain of f, if $x_1\ne x_2$, then $f\left(x_1\right)\ne f\left(x_2\right)$.”

Description:

Suppose that the function $f\left(x\right)$ is one-to-one.

Note that a function is one-to-one if no two elements in the domain of the function correspond to the same element in the range.

Clearly, by the above result, if $x_1\ne x_2$, then $f\left(x_1\right)\ne f\left(x_2\right)$.

Therefore, the correct option is $\underset{\_}{c}$.