Answer:
D. [tex]f(x)= x+3[/tex] and [tex]g(x)=\sqrt{x}[/tex]
Step-by-step explanation:
We are given that,
Composition of two functions f and g is given by,
[tex]h(x) = (g\circ f)(x) = \sqrt{x+3}[/tex].
According to the options:
A. [tex]h(x) = (g\circ f)(x) = g(3x)=\sqrt{3x}[/tex]
B. [tex]h(x) = (g\circ f)(x) = g(x)=x+3[/tex]
C. [tex]h(x) = (g\circ f)(x) = g(\sqrt{x})=\sqrt{x}+3[/tex]
D. [tex]h(x) = (g\circ f)(x) = g(x+3)=\sqrt{x+3}[/tex]
Thus, we see that, option D is correct.
Hence, [tex]f(x)= x+3[/tex] and [tex]g(x)=\sqrt{x}[/tex] is a possible decomposition of h(x).
