A function \( f(x) = x + 1 \) is a one-to-one (injective) function. A function is one-to-one if, for distinct elements in the domain, the corresponding elements in the range are also distinct. In other words, no two different elements in the domain map to the same element in the range.
Let's consider the function \( f(x) = x + 1 \). Suppose \( f(a) = f(b) \) for some \( a \) and \( b \) in the domain. Then,
\[ a + 1 = b + 1 \]
Subtracting 1 from both sides,
\[ a = b \]
This implies that if \( f(a) = f(b) \), then \( a = b \), showing that distinct elements in the domain have distinct images in the range. Therefore, \( f(x) = x + 1 \) is a one-to-one function.
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