Given ƒ(x) = x + 1 and h(x) = 2x – 3, find (ƒ + h)(x).
x+1 + 2x-3 =
To find (ƒ + h)(x), we need to add the functions ƒ(x) and h(x) together.
The function ƒ(x) is defined as ƒ(x) = x + 1, and the function h(x) is defined as h(x) = 2x – 3.
To get (ƒ + h)(x), we add the corresponding terms of the two functions together.
(ƒ + h)(x) = ƒ(x) + h(x)
Now, substituting the given functions into the equation, we have:
(ƒ + h)(x) = (x + 1) + (2x – 3)
To simplify, combine like terms:
(ƒ + h)(x) = x + 2x + 1 – 3
Next, combine the x terms and the constant terms:
(ƒ + h)(x) = 3x - 2
Therefore, the sum of the two functions ƒ(x) = x + 1 and h(x) = 2x – 3 is (ƒ + h)(x) = 3x - 2.