Question

The domain of ​(f​g)(x) consists of the numbers x that are in the domains of both f and g.

Answer 1

The statement "The domain of (fg)(x) consists of the numbers x that are in the domains of both f and g" is FALSE.

Domain is the values of x in the function represented by y=f(x), for which y exists.

THe given statement is "The domain of (fg)(x) consists of the numbers x that are in the domains of both f and g".

Now we assume the $g(x)=x+2$ and $f(x)=\frac{1}{x-6}$

So here since g(x) is a polynomial function so it exists for all real x.

$f(x)=\frac{1}{x-6}$  does not exists when $x=6$, so the domain of f(x) is given by all real x except 6.

Now,

$(fg)(x)=f(g(x))=f(x+2)=\frac{1}{(x+2)-6}=\frac{1}{x-4}$

So now (fg)(x) does not exists when x=4, the domain of (fg)(x) consists of all real value of x except 4.

But domain of both f(x) and g(x) consists of the value x=4.

Hence the statement is not TRUE universarily.

Thus the given statement about the composition of function is FALSE.

Learn more about Domain here -

brainly.com/question/2264373

#SPJ10