# Problem Solving

## No 01

Functions $$f$$ and $$g$$ are defined as follows:

$$f : x \rightarrow (x - 1)^2, \: x \in R, \: x \geq 1$$

$$g : x \rightarrow \dfrac{x}{1 + x}, \: x \in R, \: x \geq 0$$

(i) Find the range of g

(ii) Define the inverse function $$f^{-1}$$

(iii) Define the composite function $$gf$$