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1 vote
If f(x) =

3x-2
———
6
which of the following is the inverse of f(x)?
O A. f-'(x) =
x= 2x
O B. F'(x) = 6x-2
O c. f'(x) = 6**2
OD. F'(x) = 2x32

If f(x) = 3x-2 ——— 6 which of the following is the inverse of f(x)? O A. f-'(x) = x-example-1
User Arun Pal
by
7.5k points

2 Answers

6 votes

Answer:

i thin correct answer is b

User Sander Aernouts
by
8.7k points
4 votes

The inverse of f(x) is (option C)


$f^(-1)(x)=(6x+2)/(3)$

To find the inverse of the function
\( f(x) = (3x - 2)/(6) \), we perform the following steps:

1. Swap x and y to express the inverse function:
\( y = (3x - 2)/(6) \).

2. Solve for x : Multiply both sides by 6 to get rid of the fraction:

6y = 3x - 2 .

3. Add 2 to both sides:


\( 6y + 2 = 3x \).

4. Divide by 3 to solve for x :


\( x = (6y + 2)/(3) \).

This gives us the inverse function
\( f^(-1)(y) = (6y + 2)/(3) \). Simplifying the expression, we get:


\[ f^(-1)(y) = 2y + (2)/(3) \]

Since this expression is in terms of y , to write it in the usual function form, replace y with x :


\[ f^(-1)(x) = 2x + (2)/(3) \]

User Krlzlx
by
8.6k points

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