The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. which of the following describes the domain of (g o f) (x)?
all real values except x not-equals negative 3 and the x for which f (x) not-equals 7
all real values except x not-equals negative 3 and the x for which f (x) not-equals negative 3
all real values except x not-equals 7 and the x for which f (x) not-equals 7
all real values except x not-equals 7 and the x for which f (x) not-equals negative 3

The last is the correct option

"all real values except x not-equals 7 and the x for which f (x) not-equals negative 3"

Step-by-step explanation:

Domain and Range of Functions

Given the function f(x), the domain of f is the set of all the values that x can take such f(x) exists. The range of f is the set of all the values that f takes.

We have a problem where we have to find the domain of a composite function. Let's recall that being f and g real functions, then

is the composite function of f and g.

We know the domain of f is the set of all real values except 7, and the domain of g is the set of all real values except –3.

Since f is the innermost function, the domain of the composite function is directly restricted by the domain of f. So, x cannot be 7.

Now, g takes f as its independent variable, and we know the domain of g excludes -3. It can be found that f(x) cannot be -3 because it will cause g not to exist.

Thus, the domain of is

All real numbers except x=7 and those where f(x)=-3

The last is the correct option

sorry, i can't understand your question. will later if you describe more clearly!

: )

b.-4 units

all you   do is count how many times you move