Use the following to answer questions :
f(x) = and g(x) = 3x - 5
-State the domain of h(x) = (g ? f)(x).
A) x $\in$ [0, ?)
B) x $\in$ [-2, ?)
C) x $\in$ [1, ?)
D) x $\in$ (-?, ?)

Question

Use the following to answer questions :
f(x) =  and g(x) = 3x - 5
-State the domain of h(x) = (g ? f)(x).
A) x $\in$ [0, ?) 
B) x $\in$ [-2, ?) 
C) x $\in$ [1, ?) 
D) x $\in$ (-?, ?)

Quizplus · Accepted Answer

The domain of h(x) is determined by the domain of the composition function g ◦ f, which is the set of all x in the domain of f such that f(x) is in the domain of g. 
Since g(x) is defined for all real numbers, we only need to find the values of x that make f(x) in the domain of g. It can be seen that f(x) is a hexadecimal number with 32 digits, which cannot be negative. Therefore, the domain of f is the set of non-negative real numbers, i.e. [0, ∞). 
When we apply g to f(x), we get g(f(x)) = 3f(x) - 5. This function is defined for all real numbers. Thus, the domain of h(x) is [0, ∞). Therefore, the correct answer is B, x ∈ [−2, ∞).

Use the Following to Answer Questions : F(x) = ∈\in∈ [0, ?) B) X

Use the Following to Answer Questions :
F(x) = $\in$ [0, ?)
B) X