Detection of elementary functions

Detect and write the corresponding elementary functions

a) $f(x)=e^{2\sin x}$

b) $f(x)=\sqrt{\sin(x^2-x+2)}$

a) $g(x)=e^x; \ \ h(x)=2x; \ \ t(x)=\sin(x)$

The composition is the following one: $f(x)=g(h(t(x)))$

b) $g(x)=\sqrt{x}; \ \ h(x)=\sin(x); \ \ t(x)=x^2-x+2$

In this case the function $t(x)$ is not an elementary function, but it is a sum of elementary functions. How does the composition work?

The composition is the following one: $f(x)=g(h(t(x)))$

a) $g(x)=e^x; \ \ h(x)=2x; \ \ t(x)=\sin(x) \Rightarrow f(x)=g(h(t(x)))$

b) $g(x)=\sqrt{x}; \ \ h(x)=\sin(x); \ \ t(x)=x^2-x+2 \Rightarrow f(x)=g(h(t(x)))$