Answer :
To find (ƒ − g)(1) for the functions ƒ(x) = 6x and g(x) = x + 6, first find the expression (ƒ − g)(x) = 5x - 6, then substitute x = 1 to get the result of -1.
Finding (ƒ − g)(1):
Let's start by defining the functions given in the problem:
- ƒ(x) = 6x
- g(x) = x + 6
The expression (ƒ − g)(x) represents the difference between the two functions, which can be written as:
(ƒ − g)(x) = ƒ(x) - g(x)
Next, we substitute the given functions into this expression:
(ƒ − g)(x) = 6x - (x + 6)
Now, distribute the negative sign through the parentheses:
(ƒ − g)(x) = 6x - x - 6
Combine like terms:
(ƒ − g)(x) = 5x - 6
We need to find (ƒ − g)(1), so we substitute x = 1 into the simplified expression:
(ƒ − g)(1) = 5(1) - 6
Calculate the result:
- (ƒ − g)(1) = 5 - 6
- (ƒ − g)(1) = -1
The final result is -1.
