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

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If f(x) = (5x + 1) /2 
Ok, you need to find inverse function, here's how...

1. Change "f(x)" to y, to make the calculations easier. y = (5x + 1) /2 2. Switch x and y: x = (5y + 1) /2 3. Solve for y: x = (5y + 1) /22x = 5y + 12x - 1 = 5y(2x - 1) / 5 = y 4. Change "y" to f-1(x) (2x - 1) / 5 = f-1(x) Now, plug in 8 for x to get the  (2*8 - 1) / 5 = (16 - 1) / 5 = 15/5 = 3

Hope this helps :)