SOLUTION: If f(x)=5x-12, find a value for x so that f^-1(x)=f(x+1).

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Question 1029544: If f(x)=5x-12, find a value for x so that f^-1(x)=f(x+1).
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
For f(x) = 5x - 12, we have f(x+1) = 5(x+1) - 12 = 5x - 7
We need to find the inverse now...
y = 5x - 12
x = 5y - 12
5y = x + 12
y = (1/5)(x + 12)
f^(-1)(x) = (1/5)(x + 12)
Now set these equal and get
(1/5)(x + 12) = 5x - 7
x + 12 = 25x - 35
37 = 24x
x = 37/24