Question

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

Answer 1

`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)`