Answer:
D
Explanation:
Recall that for a function
such that
, where
is the Domain and
is the Codomain, the function has a inverse, if and only if,
exist an unique
such that
.
![\therefore f^(-1)(y)=x \iff f(x)=y](https://img.qammunity.org/2022/formulas/mathematics/college/cl3sr2qn2wrn1vkg59qcefsue16ux2wny4.png)
Therefore, the inverse of
for
is
![f^(-1) =3-7x](https://img.qammunity.org/2022/formulas/mathematics/college/i3cy1bmu79syrzwh6oytjgpwgwtp92cik2.png)
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![f(x)=(3-x)/(7) \implies y= (3-x)/(7) \implies x=(3-y)/(7)](https://img.qammunity.org/2022/formulas/mathematics/college/wt4jucnvu8qftrwq8tz7pifkkblkbp4140.png)
![x=(3-y)/(7) \implies 7x = 3-y \implies 7x -3 = -y \implies -7x +3 = y \implies f(x)=3-7x](https://img.qammunity.org/2022/formulas/mathematics/college/ovrx7k03zmi0wrwc1rzpfim1ygc60dincm.png)