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

Solution:

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

We have to find  f^-1(3).

The function can be written as f(x) = (x - 5) / 3

First replace f(x) with y.

y = (x - 5) / 3

Using the multiplicative distributive property

3y = x - 5

Next replace x with y and y with x.

3x = y - 5

y = 3x + 5

Finally replace y with f^-1 (x).

f^-1 (x) = 3x + 5

Put x = 4 in the above function,

f^-1(3) = 3(3) + 5

= 9 + 5

= 14

Verification:

(f ∘ f ^-1) (x) = x

(f ∘ f ^-1) (x)= f [ f^-1 (x)]

= f [3x + 5]

= 1/3[(3x + 5) -5]

= 1/3(3x - 0)

= 3x/3

= x

Therefore, f^-1(3) = 14.

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

Summary:

Given f(x) = the quantity of x minus 5, divided by 3, then f^-1(3) is 14.