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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Development:

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: $$f(x)=g(h(t(x)))$$

Solution:

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

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

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