Answer:
Composition: [tex]f(x)\,^o\,h(x)=4\,\sqrt{x+4} -1[/tex]
Domain = { [tex]x\,/\,x\geq \,-4[/tex] }
Step-by-step explanation:
Given
[tex]f(x)=4\,x-1\,\,\, and \,\,\, h(x)=\sqrt{x+4}[/tex]
The requested composition becomes:
[tex]f(x)\,^o\,h(x)=f(h(x))\\f(x)\,^o\,h(x)=f(\sqrt{x+4} )\\f(x)\,^o\,h(x)=4\,\sqrt{x+4} -1[/tex]
Then the Domain consists of all Real x-values for which the function is defined. In this case, the function is defined for all x-values for which the square root is defined, that is all x values for which:
[tex]x+4\geq \,0[/tex] (so the square root is defined in the Real number system)
This means [tex]x\geq \,-4[/tex]
The Domain is then all the Real x-values such that [tex]x\geq \,-4[/tex]
