If ƒ (x) = 3x + 1, then ƒ (a + h) - ƒ (a) =

If ƒ (x) = 3x + 1, then ƒ (a + h) - ƒ (a) = 3h

Step-by-step explanation:

Given ƒ (x) = 3x + 1, then to calculate ƒ (a + h) - ƒ (a), you need to replace "x" for (a + h) and a, respectively.

So ...

f (a + h) = 3 (a + h) + 1

and

f (a) = 3a + 1

Then

ƒ (a + h) - ƒ (a) = 3 (a + h) + 1 - [3a + 1] = 3a + 3h + 1 - 3a - 1 = 3h.

So, ƒ (a + h) - ƒ (a) = 3h