Question

Given f(x) = the quantity of 3x minus 1, divided by 2 , solve for f−1(4)

Answer 1

f(x)=(3x−1)/2<----Starter
y = (3x-1)/2
switch x and y
x = (3y-1)/2
2x = 3y-1
2x+1 =3y
y = 2/3*x + 1/3
f^(-1) (x) = 2/3*x + 1/3
f^(-1) (4) = 2/3*4 + 1/3 = 8/3 + 1/3 = 9/3 = 3

I hope this helps. ;)

Answer 2

`f^(-1)(4)=3`

Explanation:

we need to find f(x) , which is stated as " the quantity of 3x minus 1, divided by 2"

the quantity of 3x minus 1 which means, 3x - 1

and then divided by 2 gives,

`(3x-1)/(2)`

so,

`y=f(x)=(3x-1)/(2)`

to find inverse of f(x) , we switch x and y,

`x=(3y-1)/(2)`

multiply both the sides by 2, in above expression

`2x=3y-1`

add both the sides by 1, in above expression

`2x+1=3y`

now, divide above by 3, in above expression

`(2x+1)/(3)=y`

hence
`f^(-1)(x)=(2x+1)/(3)`

To find
`f^(-1)(4)`, we put x=4 in
`f^(-1)(x)=(2x+1)/(3)`

`f^(-1)(4)=(2(4)+1)/(3)`

`f^(-1)(4)=(8+1)/(3)`

`f^(-1)(4)=(9)/(3)`

`f^(-1)(4)=3`

therefore,
`f^(-1)(4)=3`