Answer:
domain [ g(t) ] = (-∞,∞)
g'(t)=9
domain [ g'(t) ] =(-∞,∞)
Step-by-step explanation:
We start by finding the domain of the function g(t)
The domain of a function is the set of all inputs over which the function has defined outputs.
In g(t) = 9t ; g(t) is define for all real numbers
domain [ g(t) ] = (-∞,∞)
For the derivative of the function we use the definition of derivative :
Given f(x)→[tex]f'(x) = \lim_{h \to \00} \frac{f(x+h)-f(x)}{h}[/tex]
In our exercise :
[tex]g'(t)= \lim_{h \to \00} \frac{g(t+h)-g(t)}{h}[/tex]
[tex]\lim_{h \to \00} \frac{9(t+h)-9t}{h} =\\ \lim_{h \to \00} \frac{9t+9h-9t}{h} =\\\lim_{h \to \00} \frac{9h}{h}\\\lim_{h \to \00} 9=9[/tex]
[tex]g'(t)=9[/tex]
domain [ g'(t) ] =(-∞,∞)
