Let $$f_1 : R \rightarrow R, f_2 :[0, \infty) \rightarrow R, f_3 : R \rightarrow R$$ and $$f_4 : R \rightarrow [0, \infty)$$ be defined by
$$f_1 (x) = \begin{cases}|x| & if x < 0,\\e^x & if x \geq 0;\end{cases}$$
$$f_2 (x) = x^2;$$
$$f_3 (x) = \begin{cases}\sin x & if x < 0,\\x & if x \geq 0;\end{cases}$$
and
$$f_4 (x) = \begin{cases}f_2(f_1(x)) & if x < 0,\\f_2(f_1(x)) - 1 & if x \geq 0.\end{cases}$$