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Which of the following functions has inv...

Which of the following functions has inverse function? `f: Zvecd efin e db yf(x)=x+2` `f: Zvecd efin e db yf(x)=2x` `f: Zvecd efin e db yf(x)=x` `f: Zvecd efin e db yf(x)=|x|`

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To determine which of the given functions has an inverse function, we need to analyze each function for its properties, specifically whether it is one-to-one (injective) and onto (surjective). A function has an inverse if and only if it is both one-to-one and onto. Let's analyze each function step by step: 1. **Function 1: \( f(x) = x + 2 \)** - **Injective (One-to-One)**: A function is injective if \( f(a) = f(b) \) implies \( a = b \). - Assume \( f(a) = f(b) \). ...
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