Question

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

Answer 1

Hey there!

Your equation will be f(x) = (5x + 1) / 2. Now, you'll need to find the inverse.

In the equation, replace f(x) with y, then switch x and y. Now, solve for y in the new equation. What equals y will be your inverse equation. 

f(x) = (5x + 1) / 2
x = (5y + 1) / 2
(x)*2 = (5y + 1 / 2)*2
2x = 5y + 1
–1           –1
(2x – 1) / 5 = (5y) / 5
(2x – 1) / 5 = y

Your inverse function is f–1(x) = (2x – 1) / 5. Now, just plug in 8 for x and solve for the answer. 

f–1(x) = (2x – 1) / 5
f–1(8) = (2(8) – 1) / 5
f–1(8) = (16 – 1) / 5
f–1(8) = 15 / 5
f–1(8) = 3

Your final answer will be 3. Hope this helped you out! :-)