6.8.36 Set theory

Condition: Indicate which mapping \( f_{1} \) or \( f_{2} \) is linear and find the image of the segment \( [0 ; 1] \) under the selected mapping. \[ f_{1}=\frac{x^{3}+4 x^{2}+5 x+6}{2 x^{2}+2 x+4}, \quad f_{2}=\cos 2 x \]