Given g(a)=a² - 2a - 1 and f(x)=x² - 2x, Find: a) f(a+2)-f(a)/2 b) g(a+h)-g(a)/h

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Given g(a)=a² - 2a - 1 and f(x)=x² - 2x:

Find:
a) f(a+2) - f(a)/2
b) g(a+h) - g(a)/h

a) f(a + 2) = (a + 2)^2 - 2(a + 2)
f(a + 2) = a^2 + 2a + 4 - 2a - 4

Simplify and combine like terms:
the 2a and 4's cancel, so we have:
f(a + 2) = a^2

f(a)/2 = (a^2 - 2a)/2

Subtract one from the other, we get:
a^2 - a^2/2 - a
a) a^2/2 - a
------------------------
b) g(a + h) = (a + h)^2 - 2(a + h) - 1
g(a + h) = a^2 +2ah + h^2 - 2a - 2h - 1

g(a)/2 = (a^2 - 2a - 1)/h
g(a)/2 = (a^2 - 2a - 1)/h

Subtract one from the other:
g(a+h) - g(a)/h
a^2 +2ah + h^2 - 2a - 2h - 1 - (a^2 - 2a - 1)/h

Multiply through by h
a^2h + 2ah^2 + h^3 - 2ah - 2h^2 - h - a^2 + 2a + 1