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