Every function is invertible.

Explanation

To determine whether the statement "Every function is invertible" is true or false, we can follow these steps:

### Step 1: Understand the Definition of Invertible Functions
A function is said to be invertible if there exists another function that can reverse its mapping. For a function to be invertible, it must be a bijection, meaning it is both one-to-one (injective) and onto (surjective).

### Step 2: Identify the Conditions for Invertibility
- **One-to-One (Injective)**: Each element in the domain maps to a unique element in the codomain. No two different inputs produce the same output.
- **Onto (Surjective)**: Every element in the codomain is an image of at least one element from the domain.

### Step 3: Analyze the Statement
The statement claims that every function is invertible. However, not all functions meet the criteria of being bijective.

### Step 4: Provide a Counterexample
Consider the function \( f: \{1, 2, 3, 4\} \to \{2, 1, 2, 5\} \) defined as:
- \( f(1) = 2 \)
- \( f(2) = 1 \)
- \( f(3) = 2 \)
- \( f(4) = 5 \)

In this case:
- The output \( 2 \) is produced by both inputs \( 1 \) and \( 3 \). Thus, the function is not one-to-one (not injective).
- Since the function is not injective, it cannot have an inverse that is also a function.

### Step 5: Conclusion
Since we have shown that not all functions are invertible (using the counterexample), we can conclude that the statement "Every function is invertible" is **false**. Only bijective functions are invertible.

### Final Answer
The statement "Every function is invertible" is **false**.

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