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

question 9

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

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