Question

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

Answer 1

Answer:

The domain of the given equation is $D=[x|x\neq 13]$                              

Step-by-step explanation:

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

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

Solution :

We can write,

$(fog)(x)=f(g(x))$

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

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

$(fog)(x)=\frac{1+7x-91}{x-13}$

$(fog)(x)=\frac{7x-90}{x-13}$

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

i.e.   $x-13\neq0$

 $x\neq13$

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

Answer 2

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

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

so the domain ( -∞, 13)U(13,∞)