# How do you compute (fog) and (gof) if #f(x)= x/(x-2)#, #g(x)=3/x#?

##### 1 Answer

Jan 2, 2016

#### Explanation:

#f(g(x))=(3/x)/(3/x-2)#

Find a common denominator in the denominator.

#f(g(x))=(3/x)/(3/x-(2x)/x)#

Simplify.

#f(g(x))=(3/x)/((3-2x)/x)#

Multiply by

#f(g(x))=3/(3-2x)=(f@g)(x)#

To find

#g(f(x))=3/(x/(x-2))#

Recall that division is the same as multiplying by the reciprocal.

#g(f(x))=3((x-2)/x)#

Simplify for the final answer.

#g(f(x))=(3(x-2))/x=(g@f)(x)#