Given f(x) and g(x), find the indicated composition and state its domain.
-For $f ( x ) = x ^ { 2 } - 25$ and $g ( x ) = 2 x + 3$, what is the domain of $f \circ g$ ?
A) $( - \infty , \infty )$
B) $[ 0 , \infty )$
C) $( - 5,5 )$
D) $[ 5 , \infty )$

Question

Quizplus · Accepted Answer

The composition $f \circ g$ means applying g first and then f. Since $g(x) = 2x + 3$ is a linear function, its domain is all real numbers. Applying $f$ to $g(x)$ results in a quadratic function, which also has a domain of all real numbers. Thus, the domain of $f \circ g$ is $( - \infty , \infty )$.

Given F(x) and G(x), Find the Indicated Composition and State f(x)=x2−25f ( x ) = x ^ { 2 } - 25f(x)=x2−25

Given F(x) and G(x), Find the Indicated Composition and State $f ( x ) = x ^ { 2 } - 25$