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Write the operations in order for the function shown.

[tex]\[ f(x)=\sqrt[6]{\sin \left(7 x^2\right)+1} \][/tex]

A. First square the input, then take the sine, add 1, multiply by 7, then take the sixth root.

B. First square the input, then multiply by 7, take the sine, add 1, and take the sixth root.

C. First multiply the input by 7, then square it, take the sine, add 1, then take the sixth root.

D. First multiply the input by 7, then square it, take the sixth root, then take the sine, then add 1.

E. First multiply the input by 7, then take the sine, add 1, square it, then take the sixth root.

F. First square the input, then take the sine, add 1, take the sixth root, then multiply by 7.

G. First multiply the input by 7, then take the sine, add 1, take the sixth root, then square it.

H. First square the input, then multiply by 7, take the sixth root, then take the sine, then add 1.



Answer :

GinnyAnswer
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.

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