Given f(x) = the quantity of x plus 7, divided by 5, solve for f^-1(3).

Solution:

Given, f(x) = the quantity of x plus 7, divided by 5

We have to find f^-1(3).

The fundamental operations can be performed on two or more functions to give a new function as a result.

We will use inverse of function formula to solve this problem.

f(x) = (x + 7)/5

First replace f(x) with y.

y = (x + 7)/5

Next replace x with y and y with x.

x = (y + 7)/5

Solving for y, we get,

5x = y + 7

y = 5x - 7

Finally replace y with f ^-1(x).

f ^-1(x) = 5x - 7

Put x = 3,

y = 5(3) - 7

y = 15 - 7

y = 8

Verification:

(f ∘ f ^-1) (x) = x

(f ∘ f ^-1) (x) = f [f^-1(x)]

= f [5x - 7]

= [5x - 7 + 7]/5

= 5x/5

= x

Therefore, the inverse function when x = 3 is 8.

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Given f(x) = the quantity of x plus 7, divided by 5, solve for f^-1(3).

Summary:

Given f(x) = the quantity of x plus 7, divided by 5, then f^-1(3) is 8.