If the inverses of two functions are both functions, will the inverse of the product or quotient of the original functions also be a function? Example too please..
+129849 Not all products (or quotients) of the invertible functions will have inverses
Examples:
f(x) = 1/x
f(x) = 1/x^2
Both of these have inverses
Product of the original functions = 1/x^3 this is one-to-one so it has an inverse function
Quotient of the original functions = either x or 1/x.......both of these are one-to-one so both have inverse functions
However consider :
f(x) = x - 3
f(x) = x + 5
Both of these functions are one-to-one and thus have inverses
However........their product = x^2 + 2x - 15......and this is not a one-to-one function, so it will have no inverse [ unless we restrict the domain]
