Question

If ƒ(x ) = 3x + 1, then ƒ(a + h ) - ƒ(a ) = h 3 h 3 h + 2
h
3 h
3 h + 2

Answer 1

3h

Explanation:

Given function:

`f(x) = 3x + 1`

To find f(a + h), substitute x = a + h into f(x).

Similarly, to find f(a), substitute x = a into f(x).

Therefore:

`\begin{aligned}\implies f(a+h)-f(a)&=[3(a+h)+1]-[3(a)+1]\\&=[3a+3h+1]-[3a+1]\\&=3a+3h+1-3a-1\\&=3a-3a+3h+1-1\\&=3h\end{aligned}`