g(x) = 2x + 1
Find g(a + h):
g(a + h) = 2(a + h) + 1 = 2a + 2h + 1
Find g(a):
g(a) = 2(a) + 1 = 2a + 1
Find g(a + h) - g(a):
g(a + h) - g(a) = 2a + 2h + 1 - ( 2a + 1)
Distribute the negative sign:
g(a + h) - g(a) = 2a + 2h + 1 - 2a - 1
Combine like terms:
g(a + h) - g(a) = 2h
Answer: 2h
