Problems from Detection of elementary functions

Detect and write the corresponding elementary functions

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

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

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

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

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

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