Question

Explain why f (2)+ f(3) ≠ f (5)

Answer 1

The statement f(2) + f(3) ≠ f(5) implies that the values of f(2), f(3), and f(5) are not equal, indicating that the function f is not additive or linear. An example using a quadratic function is provided to illustrate the inequality.

Step-by-step explanation:

The statement f(2) + f(3) ≠ f(5) implies that the values of f(2), f(3), and f(5) are not equal. In other words, the sum of the function values at 2 and 3 is not equal to the function value at 5. This indicates that the function f is not additive or linear.

To further explain, let's assume f(x) = x^2. Then, f(2) = 2^2 = 4, and f(3) = 3^2 = 9. However, f(5) = 5^2 = 25. Clearly, 4 + 9 ≠ 25, which confirms that f(2) + f(3) ≠ f(5).

Therefore, the inequality f(2) + f(3) ≠ f(5) holds true for non-linear functions.

Answer 2

Step-by-step explanation:

We cannot determine whether f(2)+f(3) is equal to f(5) or not without any information about the function f.

For example, if f(x) = x, then f(2) + f(3) = 2 + 3 = 5, and f(5) = 5, so f(2)+f(3) = f(5).

However, if f(x) = x^2, then f(2) + f(3) = 2^2 + 3^2 = 4 + 9 = 13, and f(5) = 5^2 = 25, so f(2)+f(3) ≠ f(5).

Therefore, the relationship between f(2)+f(3) and f(5) depends on the specific function f, and cannot be determined without knowing the functional form of f.