MAT103

Franklin College

Erich Prisner

### Writing Project 11:

# The inverse function of a composed function

The inverse function of f(x) = x+1 is f^{-1}(x) = x-1. The inverse
function of g(x) = is g^{-1}(x) = x^{2}.
Can the inverse of the composed function g(f(x)) =
be expressed by the inverses of f and g? Is this true in general? Discuss also
whether or not a composed function of two 1-1 functions must be 1-1. Discuss
also special cases: Is the composed function of two (strictly)
increasing/decreasing functions again (strictly) increasing/decreasing?