Determine Algebraically Whether the Following Function Is One-To-One $| x - 5 | , \quad x \leq 5$

Multiple Choice

Determine algebraically whether the following function is one-to-one.
$| x - 5 | , \quad x \leq 5$
$| a - 5 | = | b - 5 |$

A)
$\begin{aligned}5 - a & = 5 - b \quad ; \text { one-to-one } \\- a & = - b \quad \\a & = b\end{aligned}$
$| a - 5 | = | b - 5 |$

B) $| a - 5 | = | b - 5 |$
$\begin{aligned} | a | - 5 & = | b | - 5 \\ | a | & = | b | \quad \text { one-to-one } \\ a & = b \end{aligned}$

C) $| a - 5 | = | b - 5 |$

$\begin{aligned}a + 5 & = 5 - b \quad ; \text { not one-to-one } \\a & = - b\end{aligned}$

D) $| a - 5 | = | b - 5 |$
$\begin{aligned} \\ | - 5 | - a & = | - 5 | + b ; \text { not one-to-one } \\ - a & = b \end{aligned}$

E) $| a - 5 | = | b - 5 |$
$\begin{aligned}| - 5 | - a & = | - 5 | - b ; \text { one-to-one } \\- a & = - b \\a & = b\end{aligned}$