Question

Given the function f(x) = the quantity of 5x minus 3, divided by 4, which of the below expressions is correct?. f−1(x) = The quantity of 3 minus 5x, divided by 4. . f−1(x) = The quantity of 4x plus 3, divided by 5. . f−1(x) = The quantity of 4x minus 3, divided by 5.. . f−1(x) = The quantity of 4x minus 3, divided by 5.

Answer 1

Option 2 -
`f^(-1)(x)` = The quantity of 4x plus 3, divided by 5.

Explanation:

Given : f(x) = the quantity of 5x minus 3, divided by 4

To find : Which of the below expressions is correct?

Solution :

We can write the expression as

`f(x)=(5x-3)/(4)`

Let, f(x)=y

`y=(5x-3)/(4)`

To find inverse, interchange the place of x and y and solve for y.

`x=(5y-3)/(4)`

`4x=5y-3`

`4x+3=5y`

`(4x+3)/(5)=y`

So, The inverse of f(x) is
`f^(-1)(x)=(4x+3)/(5)`

or
`f^(-1)(x)` = The quantity of 4x plus 3, divided by 5.

Therefore, option 2 is correct.

Answer 2

f(x) = [5x - 3] / 4

f[-1] (x) = {4 [f(x)] + 3 } / 5

Answer: f−1(x) = The quantity of 4x plus 3, divided by 5