Let f(x) = 1/ax+b where a and b are nonzero constants. Find all solutions to f^{-1}(x) = 0. Express your answer in terms of a and/or b.
+9466 There are a lot of ways to think about this, but here's one way.
Also I'm assuming that f(x) = 1 / (ax + b) .
f-1( x ) = 0 We want to solve for x . Apply the function f to both sides of the equation.
f( f-1( x ) ) = f( 0 )
x = f(0)
x = 1 / (a(0) + b)
x = 1 / b For f to be a function, 1/b must be the only value of f(0) .
So...
f-1( 1/b ) = 0
The only solution to f-1(x) = 0 is x = 1/b .
