Functions and Inverse

Question

Given that g(x)=4/x , x is not equal to 0 and fg(x)=2x+3 find the function f. This is composition functions/

Answer 1

Evaluate g(x), and substitute g(x) into the argument of f(x).  Perhaps this is more clear if you rename a variable.

 

g(x) = 4/x = u

 

f(u) = 2u + 3 = 2(4/x) + 3 = 8/x + 3