Question

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

Answer 1

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

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