Question

F(x) = (2x + 3) - 5, g(x) = 7 Find (f - g)(x).

a) (f-g)(x) = 2x] - 9
b) (f - g)(x) = |2x - 9
c) (f - g)(x) = 2x + 3) - 12
d) (f - g)(x) = 2x - 21 - 7​

Answer 1

To find (f - g)(x), we subtract g(x) from f(x) after simplifying f(x). The calculation results in (f - g)(x) = (2x - 2) - 7, which simplifies to 2x - 9, making option b) the correct answer.

Step-by-step explanation:

The question asks for the difference of two functions, f(x) and g(x), which is expressed as (f - g)(x). To find this, we subtract the function g(x) from f(x).

Given f(x) = (2x + 3) - 5 and g(x) = 7, we can simplify f(x) first:

f(x) = (2x + 3) - 5 = 2x + 3 - 5 = 2x - 2

Now we calculate (f - g)(x):

(f - g)(x) = f(x) - g(x) = (2x - 2) - 7 = 2x - 2 - 7 = 2x - 9

Therefore, the correct answer is option b) (f - g)(x) = 2x - 9.