Given f(x) = the quantity of 4x plus 1, divided by 3, solve for f^-1(3).

Solution:

Given, f(x) = the quantity of 4x plus 1, divided by 3

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

f(x) = (4x + 1)/3

First replace f(x) with y.

y = (4x + 1)/3

Next replace x with y and y with x.

x = (4y + 1)/3

Solving for y, we get,

3x = 4y + 1

4y = 3x - 1

y = 3x/4 - 1/4

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

f ^-1(x) = 3x/4 - 1/4

Put x = 3,

y = 3(3)/4 - 1/4

y = (9 - 1)/4

y = 8/4

y = 2

Verification:

(f ∘ f ^-1) (x)= x

(f ∘ f ^-1) (x)= f [f ^-1(x)]

= f [3x/4 - 1/4]

= (4[3x/4 - 1/4] + 1)/3

= 3x/3

= x

Therefore, the inverse function when x = 3 is 2.

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Given f(x) = the quantity of 4x plus 1, divided by 3, solve for f^-1(3).

Summary:

Given f(x) = the quantity of 4x plus 1, divided by 3, then f^-1(3) is 2.