Question

Please help with this certain math problem

Answer 1

Answer: For this real-valued function;

$fog = 2\sqrt{x-1} + 1\\ Domain = [1, )$

Step-by-step explanation:

COMPOSITE FUNCTION

If f and g are functions, then the composite function or composition, of g and f is defined by

$( f o g ) (x) = f(g(x))$

Given the functions $f(x)=2x+1$ , $g(x)=\sqrt{x-1}$,

Now composition for this;

$fog = f(g(x))f(g(x)) = f(\sqrt{x-1} )$

$f(\sqrt{x-1})$means we are to interchange variable x in $f(x)$ with the function $\sqrt{x-1}$

$f(\sqrt{x-1}) = 2(\sqrt{x-1})+1f(\sqrt{x+1}) = 2(\sqrt{x-1})+1fog = 2(\sqrt{x-1})+1$

The function inside the square root, x-1, must be more significant than or equal to zero (x-10), for the function to exist on any real-valued function.

$if, x-1 \geq 0\\x\geq 0+1\\x \geq 1$

As a result, the range of the variable x must only include values that are larger than or equal to 1.

Hence, Domain = [1, )

DOMAIN = The domain of $fog$ is the set of all numbers $x$ in the domain of $g$ such that $g(x)$  is in the domain of $f$.

Learn more about Composition and Domain here; https://brainly.com/question/6390405

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