Let f(x)=1/(ax+b) where a and b are nonzero constants. Find all solutions to f^(-1)(x) = 1. Express your answer in terms of a and/or b.
y = 1 / ( ax + b) get x by itself
y ( ax + b) = 1
ay x + by = 1
ay x = 1 - by
x = ( 1 - by) /( ay) swap x and y
y = (1 - bx) / (ax) = f-1 (x)
1 = (1 - bx) / (ax)
ax = 1 - bx
ax - bx = 1
x ( a - b) = 1
x = 1 / ( a - b )
