Question

if f(x) = x2 – 25 and g(x) = x – 5, what is the domain of(f/g)(x) ?all real values of xall real values of x except x = 5all real values of x except x = –5all real values of x except x = 5 and x = –5

Answer 1

so, f of g of x or f(g(x)) equals f(x) with g(x) plugged into all the x values of f(x)

I know that sounds really weird so Ill just show you:

$f(x)=x^{2}-25$
$g(x)=x-5$
$f(g(x))=g(x)^{2}-25$
$f(g(x))=(x-5)^{2}-25$

The domain is just the numbers on the x axis you can plug into the function and still get a number out. For example: you can plug 10 into x for this function and get:
$f(g(x))=(10-5)^{2}-25$
$f(g(x))=5^{2}-25=0$

See that you get a number out? That means that 10 would be in the domain.
On the other hand look at this function:

$\frac{10-x}{x-2}$

What number makes this function not work? The key is remembering the rule that you cannot ever divide by zero. So what number could you plug in to this function that would make it so you would divide by zero? The answer is two. So for this equation the domain is all real numbers except for the number 2.

Hope this helps