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.