Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Given,

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

$\implies f(x) = \frac{4x-2}{3}$ -----(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),

$y=\frac{4x-2}{3}$

By interchanging x and y,

$x=\frac{4y-2}{3}$

$3x = 4y - 2$

$-4y = -2 - 3x \implies y = \frac{3x+2}{4}$

By replacing y by $f^{-1}(x)$

$f^{-1}(x)=\frac{3x+2}{4}$

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

Answer 2

Answer:

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

Step-by-step 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.