Question

problem. 3 : find the derivative of the function using the definition of the derivative.
$f(x) = 2x - 2$
$f(x) = 2$
problem. 3.1 : state the domain of the function. (enter your answer using interval notation.)
$left( -\infty, \infty \
ight)$
problem. 3.1.1 : state the domain of its derivative. (enter your answer using interval notation.)
$left( \square, \square \
ight)$

Explanation:

Step1: Analyze the derivative function

The derivative of \( f(x) = 2x - 2 \) is \( f'(x)=2 \), which is a constant function.

Step2: Determine the domain of a constant function

A constant function (like \( y = 2 \)) is defined for all real numbers. In interval notation, the set of all real numbers is \( (-\infty, \infty) \).

Answer:

\((-\infty, \infty)\)