Question

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

Answer 1

(f*g)(x)= (x+7)(1/x-13)

= (x+7)/(x-13)

so the domain ( -∞, 13)U(13,∞)

Answer 2

The domain of the given equation is
`D=[x|x\\eq 13]`

Explanation:

Given : If
`f(x)=x+7` and
`g(x)=(1)/(x-13)`

To find : What is the domain of
`(fog)(x)`?

Solution :

We can write,

`(fog)(x)=f(g(x))`

`(fog)(x)=f((1)/(x-13))`

`(fog)(x)=(1)/(x-13)+7`

`(fog)(x)=(1+7x-91)/(x-13)`

`(fog)(x)=(7x-90)/(x-13)`

We have seen that
`(fog)(x)` to be defined when denominator cannot be zero.

i.e.
`x-13\\eq0`

`x\\eq13`

So, The domain of the given equation is
`D=[x|x\\eq 13]`