Question

hello I need help with question 2 attached is the tables created in question one which I need to base question 2 off of. 2. Find the domain and range of f(x)  and g(x) . Do you see any relationship between the domain of f(x) and the range of g(x) ? Do you see any relationship between the domain of g(x)  and the range of f(x)?

Answer 1

The given functions are:

$\begin{gathered} f(x)=3x+2 \\ g(x)=\frac{x-2}{3} \end{gathered}$

The domain is the set of all possible values that the independent variable (x) can take.

The range is the set of values that the function will take.

For these functions, the domain is all real numbers since they both will work with any positive or negative number (-∞,∞). Thus, the range is the same, all real numbers (-∞,∞).

But, for the purpose of the question let's analyze the interval you took for the table of values:

For f(x) function, you take x-values from -3 to 3, then the domain in this interval is [-3,3] and the range is the output values (f(x)), then the range is [-7,11].

For g(x) function, you take x-values from -7 to 11, then the domain in the interval is [-7,11] and the range (the g(x) values obtained) is [-3,3].

As can be noticed, in the interval the domain of the f(x) functions is the same as the range of the g(x) function, and the domain of the g(x) function is the same as the range of f(x) function. This happens because g(x) is the inverse function of f(x).