Question

Goodmorning, i just need an answer for 1A & 1B , 1c is already answered

Answer 1

Given:

`g(x)=(1)/(4)\sqrt[3]{x-3}+2`

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

`g(9)=(1)/(4)\sqrt[3]{9-3}+2`

Simplify the expression

`\begin{gathered} g(9)=(1)/(4)\sqrt[3]{3}+2_{} \\ g(9)=(1)/(4)*1.44+2 \\ g(9)=2.36\text{ million} \end{gathered}`

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

`\lbrack0,24)`

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

`\lbrack1.639,2.69)`

The range is in millions