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

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Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

f(x) = The quantity of 3x minus 4, divided by 5

Mathematically,

[tex]f(x)=\frac{3x-4}{5}[/tex]

We need to find the inverse of f , so,

Let f(x)=y

[tex]\frac{3x-4}{5}=y\\\\3x-4=5y\\\\3x=5y+4\\\\x=\frac{5y+4}{3}[/tex]

Now, replace y with x,

[tex]y=\frac{5x+4}{3}\\\\f^{-1}(x)=\frac{5y+4}{3}[/tex]

So, [tex]f^{-1}(x)[/tex]= The quantity of 5x plus 4, divided by 3.

Hence, Option 'A' is correct.