The composition of function is commutative.

Explanation

To determine whether the composition of functions is commutative, we need to analyze the functions and their compositions step by step.

### Step 1: Define the Functions
Let’s define two functions:
- \( f(x) = x^2 \)
- \( g(x) = x + 1 \)

### Step 2: Compute the Composition \( f(g(x)) \)
Now, we will compute the composition \( f(g(x)) \):
- First, substitute \( g(x) \) into \( f(x) \):
\[ f(g(x)) = f(x + 1) \]
- Now, apply the function \( f \):
\[ f(x + 1) = (x + 1)^2 \]
- Expanding this gives:
\[ (x + 1)^2 = x^2 + 2x + 1 \]
Thus, \( f(g(x)) = x^2 + 2x + 1 \).

### Step 3: Compute the Composition \( g(f(x)) \)
Next, we will compute the composition \( g(f(x)) \):
- Substitute \( f(x) \) into \( g(x) \):
\[ g(f(x)) = g(x^2) \]
- Now, apply the function \( g \):
\[ g(x^2) = x^2 + 1 \]

### Step 4: Compare the Results
Now we compare the two results:
- \( f(g(x)) = x^2 + 2x + 1 \)
- \( g(f(x)) = x^2 + 1 \)

Clearly, \( f(g(x)) \neq g(f(x)) \).

### Conclusion
Since \( f(g(x)) \) is not equal to \( g(f(x)) \), we conclude that the composition of functions is not commutative. Therefore, the statement "The composition of function is commutative" is **false**.

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