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Math  /  Algebra

QuestionQuestion 10 (1 point) Find g∘fg \circ f and the domain of the composite function. f(x)=x2+4,g(x)=xf(x)=x^{2}+4, g(x)=\sqrt{x} a (x−4)4\sqrt{(x-4)^{4}} Domain of g∘fg \circ f : all real numbers xx b (x−4)4(x-4)^{4} Domain of g∘fg \circ f : all real numbers xx c x2+4\sqrt{x^{2}+4} Domain of g∘fg \circ f : all real numbers xx d (x+4)4\quad(x+4)^{4} Domain of g∘fg \circ f : all real numbers xx e (x+4)4\sqrt{(x+4)^{4}} Domain of g∘fg \circ f : all real numbers xx

Studdy Solution
Determine the domain of g∘f g \circ f .
The function g(x)=x g(x) = \sqrt{x} is defined for x≥0 x \geq 0 . Therefore, f(x) f(x) must satisfy: x2+4≥0 x^2 + 4 \geq 0
Since x2+4 x^2 + 4 is always positive for all real numbers x x (as x2≥0 x^2 \geq 0 and adding 4 makes it strictly positive), the domain of g∘f g \circ f is all real numbers.
The correct answer is: c x2+4\sqrt{x^{2}+4} with Domain of g∘f g \circ f : all real numbers x x .

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