Answer: 2h
Step-by-step explanation:
1) Given: g (x) = 2x + 2, find g (a + h) - g (a)
2) First, replace x by a + h:
g(a + h) = 2 (a + h) + 2 = 2a + 2h + 2
3) Second, replace x by a:
g(a) = 2a + 2
4) Subtract g(a+h) - g(a)
2a + 2h + 2 - (2a + 2) = 2a + 2h + 2 - 2a - 2 = 2h
Answer: 2a
Additional explanation:
This operation is the first step the function known as derivative, since derivative is defined as:
g'(x) = limit when h → 0 of [g( x + h) - g(h)] / h
Since, you have shown that the numerator is 2h, the limit is 2h/h = 2.
And now you know that the derivative of g(x) = 2x + 2 is 2.