Let f(x) = x^2 + 9 and let g(x) = f(x - 2).
(a) Write the rule of g and simplify.
g(x) =x^2-4x+13
(b) Find the difference quotient of f(x).
Find the difference quotient of g(x).

(c) Let d(x) denote the difference quotient of f(x). Determine whether d(x - 2) is the difference quotient of g(x).

Let f(x) = x2 + 9 and let g(x) = f(x - 2).
(a) Write the rule of g and simplify.
g(x)=
(b) Find the difference quotient of f(x).
Find the difference quotient of g(x).

Let f(x) = x^2 + 9 and let g(x) = f(x - 2).
(a) Write the rule of g and simplify.
g(x) =x^2-4x+13
(b) Find the difference quotient of f(x).
Find the difference quotient of g(x).

(c) Let d(x) denote the difference quotient of f(x). Determine whether d(x - 2) is the difference quotient of g(x).


You do not have to keep reposting. It was noticed the first time. Allow folks time to get around.

a: looks good.

b: The difference quotient of g(x) is the definition of a derivative.

\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}

\lim_{h\to 0}\frac{(x+h)^{2}-4(x+h)+13-(x^{2}-4x+13)}{h}

Simplify and take the limit, and it should give the derivative of

x^{2}-4x+13

Apply the same thing to f(x) to find its DQ.