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)#