Find the domain of the composite function f $f ^ { \circ } g $
-$$f ( x ) = \sqrt { x } ; \quad g ( x ) = 5 x + 10$$
A) $\{ x \mid x \geq 0 \}$
B) $\{ x \mid x \leq - 2$ or $x \geq 0 \}$
C) $\{ x \mid x \geq - 2 \}$
D) $\{ x \mid x$ is any real number $\}$

Question

Quizplus · Accepted Answer

The composite function $f(g(x)) = \sqrt{5x + 10}$ requires the argument $5x + 10$ to be non-negative for the square root to be defined in the real number system. Solving $5x + 10 \geq 0$ gives $x \geq -2$, which defines the domain of the composite function.

Find the Domain of the Composite Function F f∘gf ^ { \circ } g f∘g

Find the Domain of the Composite Function F $f ^ { \circ } g$