Question

Given f (x)=3x-1/2 solve for f^-1 (4)

Answer 1

3

Explanation:

Answer 2

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

Explanation:

Given : Expression
`f(x)=(3x-1)/(2)`

To find : The inverse of the expression ?

Solution :

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

Let, h(x)=y then
`y=(3x-1)/(2)`

For inverse we replace the value of x and y and find the value of y in terms of x.

Replace the value of x and y,

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

Cross multiply,

`2x=3y-1`

Adding 1 both side,

`2x+1=3y`

Dividing by 3 both side,

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

The inverse of the f(x) is
`f^(-1)(x)=(2x+1)/(3)`

Put x=4,

`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`