Determine whether the function is one-to-one. $$y = \frac { 2 } { 5 } x$$
A) No, it isn't one-to-one.
B) Yes, it is one-to-one.

Question

Quizplus · Accepted Answer

A function is one-to-one if no two different inputs produce the same output. In other words, every output is paired with only one input. For the given function, every input x is paired with a unique output y, so it is one-to-one. Suppose we have two different inputs $x_1$ and $x_2$ such that $y_1=y_2$. Then, $\frac{2}{5}x_1=\frac{2}{5}x_2$. Multiplying by $\frac{5}{2}$ on each side, we get $x_1=x_2$, which implies that $y_1$ and $y_2$ were produced by different input values. Thus, the function is one-to-one.

Determine Whether the Function Is One-To-One y=25xy = \frac { 2 } { 5 } xy=52​x

Determine Whether the Function Is One-To-One $y = \frac { 2 } { 5 } x$