Given:
[tex]g(x)=\frac{1}{4}\sqrt[3]{x-3}+2[/tex]
The function represents the number of users in millions who logged into a website since midnight.
1a. How many users have logged in by 9 am?
at 9am x = 9
Substitute x = 9 into g(x)
This gives
[tex]g(9)=\frac{1}{4}\sqrt[3]{9-3}+2[/tex]
Simplify the expression
[tex]\begin{gathered} g(9)=\frac{1}{4}\sqrt[3]{3}+2_{} \\ g(9)=\frac{1}{4}\times1.44+2 \\ g(9)=2.36\text{ million} \end{gathered}[/tex]
Therefore, 2360000 users have logged into the website by 9 am.
1b Domain and range of the function.
The domain of the function is the set of all input values for which the function is real and defined.
The values of x in g(x) starts from midnight
Hence at midnight x = 0, there are 24 hours in a day
Hence the domain of g(x) is
[tex]\lbrack0,24)[/tex]
Range
The range of the function is the set of values of the dependent variables for which a function is defined
Since the function g(x) is defined for all dependent variables x
Then the range of the function is
[tex]\lbrack1.639,2.69)[/tex]
The range is in millions
