Question

Let f and g be two invertible functions such that f^-1(x)=5/x+4 and g(x)=4(x-2). Find f(g(5)).

Show your steps please so I can see how to do it. Thank you! :)

Answer 1

if the inverse is
y = 5/(x+4) , then the inverse of the inverse (the original) is
x = 5/(y+4)
xy + 4x = 5
y = (5-4x)/x
so we have
f(x) = (5-4x)/x and g(x) = 4(x-2)

g(5) = 4(5-2) = 12
f(g(5))
= f(12) = (5-48)/12 = -43/12