7
QuizMultiple Choice

Composition of Functions — Quiz

Question 7 • Mathematics III

Which description best explains the domain of open paren g circ f close paren times x ?

Answer
A
the elements in the domain of g of x for which g of f of x is defined
B
the elements in the domain of f of x for which g of f of x is defined
C
the elements in the domain of g of x for which g of f of x is not zero
D
the elements in the domain of f of x for which g of f of x is not zero

Explanation

For the composition (g ∘ f)(x), first f must be defined at x, and then g must be defined at the value f(x). So its domain consists of inputs in the domain of f for which g(f(x)) is defined. That is the description in choice A.

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