Find the derivative of the function using the definition of derivative. g(x) = 5 − x (1) find g'(x) (2) state the domain of the function. (enter your answer using interval notation.) (3) state the domain of its derivative. (enter your answer using interval notation.)

The derivative of given function g(x) is

g'(x)=-1

Domain of function g(x) is (-∞,∞)

Domain of derivative is  (-∞,∞)

Given :

Lets find derivative using definition of derivative

Derivative g'(x)=-1

g(x) is a linear function . for all linear function the domain is set of all real numbers

Domain of function g(x) is (-∞,∞)

Derivative function g'(x) =-1. For all values of x  the value of y is -1

So domain is set of all real numbers

Domain of derivative is  (-∞,∞)

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Answer is contained in the explanation

Step-by-step explanation:

g(x)=5-x has domain all real numbers (you can plug an a number and always get a number back)

So in interval notation this is

g'(x)=-1 has domain all real numbers (the original function had domain issues... and no matter the number you plug in you do get a number, that number being -1)

So in interval notation this is

ok

step-by-step explanation: