Question

If f(x)=x+7 and g(x)= 1 divided by x-13, what is the domain of (f•g)(x)?

Answer 1

Hello!

The answer is:

The domain of the function is all the real numbers except the number 13:

Domain: (-∞,13)∪(13,∞)

Why?

This is a composite function problem. To solve it, we need to remember how to composite a function. Composing a function consists of evaluating a function into another function.

Composite function is equal to:

$f(g(x))=(f\circ} g)(x)$

So, the given functions are:

$f(x)=x+7\\\\g(x)=\frac{1}{x-13}$

Then, composing the functions, we have:

$f(g(x))=\frac{1}{x-13}+7$

Therefore, we must remember that the domain are all those possible inputs where the function can exists, most of the functions can exists along the real numbers with no rectrictions, however, for this case, there is a restriction that must be applied to the resultant composite function.

If we evaluate "x" equal to 13, the denominator will tend to 0, and create an indetermination since there is no result in the real numbers for a real number divided by 0.

So, the domain of the function is all the real numbers except the number 13:

Domain: (-∞,13)∪(13,∞)

Have a nice day!