Find the domain of the composite function f∘g.
-$$f ( x ) = \sqrt { x } ; \quad g ( x ) = 6 x + 6$$
A) $[ - 1 , \infty )$
B) $[ 0 , \infty )$
C) $( - \infty , - 1 ]$ or $[ 0 , \infty )$
D) $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The composite function $f(g(x)) = \sqrt{6x + 6}$ requires the inside of the square root, $6x + 6$, to be non-negative. Solving $6x + 6 \geq 0$ gives $x \geq -1$, so the domain is $[ - 1 , \infty )$.

Find the Domain of the Composite Function F∘g f(x)=x;g(x)=6x+6f ( x ) = \sqrt { x } ; \quad g ( x ) = 6 x + 6f(x)=x​;g(x)=6x+6

Find the Domain of the Composite Function F∘g $f ( x ) = \sqrt { x } ; \quad g ( x ) = 6 x + 6$