Given f(x)=1/(x-1), and g(x)=2/x, how do you find f(g(x))?

1 Answer
Jun 4, 2017

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

Explanation:

To find f(g(x)), simply plug g(x) into x in the equation for f(x):
f(g(x))=1/((2/x)-1)
Simplify this by finding a common denominator for the denominator:
1/((2/x)-(x/x)
Simplify: 1/((2-x)/x)
Clear the fraction by using keep-change-flip: 1*(x/(2-x))
Simplify: f(g(x))=x/(2-x)