Question

Consider the following functions f(x)=2^x/2 G(x)= square root of x-3

Answer 1

Answer:

(f+g)(x)=$(2^{x} +x-3)^{\frac{1}{2} }$

Step-by-step explanation:

I assume you are asking about the question on edmuntum that wants (f+g)(x)?

in that case $2^{\frac{x}{2} }$ can be rewritten as $(2^{x})^{\frac{1}{2} }$ and $\sqrt{x-3}$ can be rewritten as $(x-3)^{\frac{1}{2} }$.

Now all that needs to be done is grouping all the terms in the same parentheses and adding in an addition sign to get $(2^{x} +x-3)^{\frac{1}{2} }$.

Answer 2

Explanation:

I don't know what your question, but I'll assume you want the composition of two functions.

Remember that:

$The \ \mathbf{composition} \ of \ the \ function \ f \ with \ the \ function \ g \ is:\\ \\ (f \circ g)(x)=f(g(x)) \\ \\ The \ domain \ of \ (f \circ g) \ is \ the \ set \ of \ all \ x \ in \ the \ domain \ of \ g \\ such \ that \ g(x) \ is \ in \ the \ domain \ of$

$f(x)=2^\frac{x}{2}} \\ \\ g(x)=\sqrt{x-3}$

Suppose in this case you want $(g \circ f)=g(f(x))$, then:

$g(f(x))=\sqrt{2^\frac{x}{2}-3}$