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.

Guest Feb 8, 2018

#1**+3 **

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 .

hectictar
Feb 8, 2018