Answer :
Explanation:
I don't know what your question, but I'll assume you want the composition of two functions.
Remember that:
[tex]The \ \mathbf{composition} \ of \ the \ function \ f \ with \ the \ function \ g \ is:\\ \\ (f \circ g)(x)=f(g(x)) \\ \\ The \ domain \ of \ (f \circ g) \ is \ the \ set \ of \ all \ x \ in \ the \ domain \ of \ g \\ such \ that \ g(x) \ is \ in \ the \ domain \ of \[/tex]
[tex]f(x)=2^\frac{x}{2}} \\ \\ g(x)=\sqrt{x-3}[/tex]
Suppose in this case you want [tex](g \circ f)=g(f(x))[/tex], then:
[tex]g(f(x))=\sqrt{2^\frac{x}{2}-3}[/tex]
Answer:
(f+g)(x)=[tex](2^{x} +x-3)^{\frac{1}{2} }[/tex]
Step-by-step explanation:
I assume you are asking about the question on edmuntum that wants (f+g)(x)?
in that case [tex]2^{\frac{x}{2} }[/tex] can be rewritten as [tex](2^{x})^{\frac{1}{2} }[/tex] and [tex]\sqrt{x-3}[/tex] can be rewritten as [tex](x-3)^{\frac{1}{2} }[/tex].
Now all that needs to be done is grouping all the terms in the same parentheses and adding in an addition sign to get [tex](2^{x} +x-3)^{\frac{1}{2} }[/tex].