Question

Given the function f(x) = The quantity of 4x minus 2, divided by 3, which of the below expressions is correct

f−1(x) = The quantity of 2 minus 4x, divided by 3.

f−1(x) = The quantity of 3x minus 2, divided by 4.

f−1(x) = The quantity of negative 4x minus 2, divided by 3.

f−1(x) = The quantity of 3x plus 2, divided by 4.

Answer 1

`f^(-1)(x)=\text{The quantity of 3x plus 2, divided by 4}`

Explanation:

Given,

f(x) = The quantity of 4x minus 2, divided by 3,

`\implies f(x) = (4x-2)/(3)` -----(1)

Since,
`f^(-1)(x)` represents the inverse of f(x),

Also, for finding the inverse of a function f(x) we follow the following steps,

Step 1 : Replace f(x) by y,

Step 2 : Interchange x and y,

Step 3 : Isolate y in the left side of the equation,

Step 4 : Replace y by
`f^(-1)(x)`

Now, from equation (1),

`y=(4x-2)/(3)`

By interchanging x and y,

`x=(4y-2)/(3)`

`3x = 4y - 2`

`-4y = -2 - 3x \implies y = (3x+2)/(4)`

By replacing y by
`f^(-1)(x)`

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

`\implies f^(-1)(x)=\text{The quantity of 3x plus 2, divided by 4}`

Answer 2

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

Explanation:

Given: f(x) = (4x -2)/3

Which is y = (4x - 2)/3

We have to find the inverse function f^-1 (x)

Replace x by y and y by x, we get

x = (4y - 2)/3

Now find the function y interms of x.

3x = 4y - 2

4y = 3x + 2

y = (3x + 2)/4

f^-1(x) = The quantity of 3x + 2, divided by 4.

Answer is D) f^-1(x) = The quantity of 3x plus 2, divided by 4.

Hope this will helpful.

Thank you.