Find the domain of the composite function f g. Write the domain in interval notation.
-$$f ( x ) = \sqrt { x } ; g ( x ) = 5 x + 20$$
A) $[ - 4 , \infty )$
B) $( - \infty , - 4 ] \cup [ 0 , \infty )$
C) $[ 0 , \infty )$
D) $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The domain of $f(g(x))$ is determined by the input $g(x) = 5x + 20$ into $f(x) = \sqrt{x}$. Since the square root function $f(x)$ requires non-negative inputs, $5x + 20 \geq 0$. Solving this inequality gives $x \geq -4$, hence the domain is $[ - 4 , \infty )$.

Find the Domain of the Composite Function F G f(x)=x;g(x)=5x+20f ( x ) = \sqrt { x } ; g ( x ) = 5 x + 20f(x)=x​;g(x)=5x+20

Find the Domain of the Composite Function F G $f ( x ) = \sqrt { x } ; g ( x ) = 5 x + 20$