Question

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 circle 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

Answer 1

answer D

Explanation:

Answer 2

The last option is correct.

Explanation:

Domain of a function means the set of values of the variable for which the given function exists.

(g circle f) (x) means g{f(x)}.

g{f(x)} will exists for all the real values of x except x = 7 and that particular x for which f(x) = -3.

Hence the domain of g{f(x)} will be all real values except x = 7 and the x for which f(x) = -3