To process the function [tex]\( f(x) = \sqrt[6]{\sin \left(7 x^2\right)+1} \)[/tex], we can follow these steps in order:
1. First square the input [tex]\( x \)[/tex], resulting in [tex]\( x^2 \)[/tex].
2. Then multiply [tex]\( x^2 \)[/tex] by 7, resulting in [tex]\( 7x^2 \)[/tex].
3. Take the sine of [tex]\( 7x^2 \)[/tex], giving [tex]\( \sin(7x^2) \)[/tex].
4. Add 1 to [tex]\( \sin(7x^2) \)[/tex], resulting in [tex]\( \sin(7x^2) + 1 \)[/tex].
5. Finally, take the sixth root of [tex]\( \sin(7x^2) + 1 \)[/tex], which gives [tex]\( \sqrt[6]{\sin(7x^2) + 1} \)[/tex].
Hence, the correct order of operations is described in option:
B. First square the input, then multiply by 7, take the sine, add 1, and take the sixth root.
