Final answer:
To calculate the image of f(9), we simply substitute 9 in place of x in the function. Therefore, f(9) = 9^2 = 81.
Step-by-step explanation:
When we are given a function that assigns an integer its square, we can represent it as f(x) = x^2, where x is the input integer. In this case, we are asked to find the image of f(9), which means we need to find the output when the input is 9.
To calculate the image of f(9), we simply substitute 9 in place of x in the function. Therefore, f(9) = 9^2 = 81.
In mathematics, a function is a relation between a set of inputs (also known as the domain) and a set of possible outputs (also known as the range). In this given question, we are dealing with a specific type of function called a square function, where the output is the square of the input.
To find the image of f(9), we need to first understand the concept of domain and range. The domain in this function is the set of all integers since the function assigns an integer as its input. The range, on the other hand, is the set of all possible outputs. In this case, since the function is a square function, the range will consist of perfect squares.
Now, to find the image of f(9), we substitute 9 for x in the function f(x) = x^2. This results in f(9) = 9^2 = 81. This means that when the input is 9, the output is 81, making 81 the image of f(9).
We can also represent this in a table:
| Input (x) | Output (f(x)) |
|-----------|---------------|
| 9 | 9^2 = 81 |
From this table, we can see that the image of f(9) is indeed 81.
In conclusion, the image of f(9) is 81. This means that when the input is 9, the output is 81. This is because the function f(x) = x^2 assigns an integer its square as its output. By understanding the concept of domain and range and substituting 9 for x in the function, we can easily find the image of f(9) to be 81.