# Given f(x) = the quantity of x minus 7, divided by 3, solve for f^{-1}(4).

**Solution:**

Given, f(x) = the quantity of x minus 7,divided by 3

We have to find f^{-1}(4).

The function can be written as f(x) = (x - 7) / 3

First replace f(x) with y.

y = (x - 7) / 3

Using the multiplicative distributive property

3y = x - 7

Next replace x with y and y with x.

3x = y - 7

y = 3x + 7

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

f^{-1} (x) = 3x + 7

Put x = 4 in the above function,

f^{-1}(4) = 3(4) + 7

= 12 + 7

= 19

**Verification:**

(f ∘ f ^{-1}) (x)= x

(f ∘ f ^{-1}) (x)= f [ f ^{-1} (x)]

= f [3x + 7]

= 1/3[(3x + 7) -7]

= 1/3(3x - 0)

= 3x/3

= x

Therefore, f^{-1}(4) = 19.

## Given f(x) = the quantity of x minus 7, divided by 3, solve for f^{-1}(4).

**Summary:**

Given f(x) = the quantity of x minus 7, divided by 3, then f^{-1}(4) is 19.

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