Question

If f (x) = x + 7 and g (x) = StartFraction 1 Over x minus 13 EndFraction, what is the domain of (f circle g) (x)? StartSet x vertical line x not-equals 6 EndSet StartSet x vertical line x not-equals negative 6 EndSet StartSet x vertical line x not-equals negative 13 EndSet StartSet x vertical line x not-equals 13 EndSet

Answer 1

Answer:

The domain of the function will be {x I x ≠ 13}.

Step-by-step explanation:

The two functions f(x) and g(x) are given to be

f(x) = x + 7 and

$g(x) = \frac{1}{x - 13}$

Now, we have to find the composite function (fog)(x).

Here, (fog)(x) = f{g(x)}

⇒ $(fog)(x) = f(\frac{1}{x - 13}) = \frac{1}{x - 13} + 7 = \frac{7x - 90}{x - 13}$

Therefore, the denominator of the function can not be zero and the domain of the function will be {x I x ≠ 13}. (Answer)

Answer 2

Answer:

The domain is  (x ∈ R - {x = 13}) this means that x can be any real number except 13.

Step-by-step explanation:

First, the domain of a function F(x) are all the possible values of x that you can input in the function.

Now, we have the functions:

f(x) = x + 7

g(x) = 1/(x - 13)

now, for the function f(x) we can use any value of x, we will not have any problem.

for g(x) the case is different, because if x = 13, we will have the case:

g(13) = 1/(13 -13) = 1/0

and we can not divide by 0, so x = 13 is not in the domain of g.

then; for the function f(g(x)) we have that the only problem is that when x = 13, so the domain is  (x ∈ R - {x = 13})