Question

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

Answer 1

i thin correct answer is b

Answer 2

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 :

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