Given f(x) = the quantity of 5x plus 1, divided by 2, solve for f^-1(8).

Solution:

Given, f(x) = the quantity of 5x plus 1,divided by 2

We have to find f^-1(8).

The function can be written as f(x) = (5x + 1) / 2

First replace f(x) with y.

y = (5x + 1) / 2

Using the multiplicative distributive property

2y = 5x + 1

Next replace x with y and y with x.

2x = 5y + 1

5y = 2x - 1

y = (1/5)(2x - 1)

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

f^-1(x) = (1/5)(2x - 1)

Put x = 8 in the above function,

f^-1(8) = (1/5)(2(8) - 1)

= (1/5)(16 - 1)

= (1/5)(15)

= 3

Verification:

(f ∘ f^-1) (x)= x

(f ∘ f^-1) (x)= f [ f ^-1 (x)]

= f [(1/5)(2x - 1)]

= 1/2[5[(1/5)(2x - 1)] + 1]

= 1/2(2x - 1 + 1)

= 1/2(2x)

= x

Therefore, f^-1(8) = 3.