To find the inverse of the function [tex]\( f(x) = \frac{1}{3} - \frac{1}{21} x \)[/tex], we need to follow these steps:
1. Rewrite the function equation in terms of [tex]\( y \)[/tex]:
[tex]\[
y = \frac{1}{3} - \frac{1}{21} x
\][/tex]
2. Swap the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse function:
[tex]\[
x = \frac{1}{3} - \frac{1}{21} y
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
- Start by isolating the term involving [tex]\( y \)[/tex]:
[tex]\[
x - \frac{1}{3} = -\frac{1}{21} y
\][/tex]
- Multiply both sides by [tex]\(-21\)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[
-21 \left( x - \frac{1}{3} \right) = y
\][/tex]
- Distribute the [tex]\(-21\)[/tex]:
[tex]\[
y = -21x + 7
\][/tex]
Thus, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[
f^{-1}(x) = 7 - 21x
\][/tex]
Therefore, the correct answer is:
B. [tex]\( f^{-1}(x) = 7 - 21x \)[/tex]
