Question

Given functions F(x)= x² -17 and G(x) = 17 - xG(x)=17−x, determine the value of (F - G)(5)(F−G)(5).

Express the result in proper mathematical notation.

Answer 1

To calculate (F - G)(5), determine F(5) and G(5) separately, then subtract G(5) from F(5). After calculation, the result is (F - G)(5) = -4.

Step-by-step explanation:

The correct answer is obtained by first defining the combination of two functions F and G. The function (F - G)(x) means we subtract function G from function F. For any value of x, this is done by subtracting the value of G(x) from F(x).

To find (F - G)(5), we calculate F(5) and G(5) separately and then subtract the latter from the former. So for F(5) = 5² - 17 = 25 - 17 = 8 and G(5) = 17 - 5 = 12. Subsequently, (F - G)(5) = F(5) - G(5) = 8 - 12 = -4.

Therefore, the result in proper mathematical notation is (F - G)(5) = -4.

First, simplify the expression inside the parentheses: F(x) - G(x) = x² - 17 - 17 + x

Combine like terms: F(x) - G(x) = x² + x - 34

Next, substitute 5 in place of x: (F - G)(5) = (5² + 5 - 34)

Calculate the values: (F - G)(5) = 25 + 5 - 34

Final calculation: (F - G)(5) = -4