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Select the correct answer.

Find the inverse of function [tex] f \left( x \right) = \frac{1}{3} - \frac{1}{21} x [/tex].

A. [tex] f^{-1} (x) = 7 - \frac{1}{21} x [/tex]

B. [tex] f^{-1} (x) = \frac{1}{7} - 21 x [/tex]

C. [tex] f^{-1} (x) = \frac{1}{7} - \frac{1}{21} x [/tex]

D. [tex] f^{-1} (x) = 7 - 21 x [/tex]



Answer :

GinnyAnswer
To find the inverse of the function [tex]\( f(x) = \frac{1}{3} - \frac{1}{21} x \)[/tex], follow these steps:

1. Express the function as [tex]\( y \)[/tex]:
[tex]\[ y = \frac{1}{3} - \frac{1}{21} x \][/tex]

2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ x = \frac{1}{3} - \frac{1}{21} y \][/tex]

3. Solve for [tex]\( y \)[/tex]:
[tex]\[ x = \frac{1}{3} - \frac{1}{21} y \][/tex]
Isolate [tex]\( y \)[/tex] by first getting rid of the constant term on the right side:
[tex]\[ x - \frac{1}{3} = -\frac{1}{21} y \][/tex]
Multiply both sides by [tex]\( -21 \)[/tex] to isolate [tex]\( y \)[/tex]:
[tex]\[ -21(x - \frac{1}{3}) = y \][/tex]
Distribute [tex]\( -21 \)[/tex]:
[tex]\[ y = -21x + 7 \][/tex]

4. Write the inverse function:
[tex]\[ f^{-1}(x) = 7 - 21x \][/tex]

So, the correct answer is:
D. [tex]\( f^{-1}(x) = 7 - 21x \)[/tex]

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