State the range

Question

If f(x) = 3x+2 / x^2+6x+9, State the range of f^-1(x).

Answer 1

The range of f^-1(x) is the same as the domain of f(x).

 

Since f(x) = (3x+2) / (x²+6x+9), domain f = {x l x²+6x+9 ≠ 0}

 

                                                               = {x l (x+3)² ≠ 0}

 

                                                               = {x l x ≠ -3} = (-∞,-3)∪(-3, ∞) = range f^-1

 

Answer 2

for f(x), the domain is all Reals except x = -3 (that's the root of the denominator, if we assume that this is a rational algebraic function IN WHICH YOU SHOULD HAVE ENCLOSED EACH OF THE NUMERATOR AND DENOMINATOR IN THEIR OWN INDIVIDUAL PARENTHESES.

 

For the inverse of f, the domain of f becomes the range of f^-1

^{and therefore I say that the range requested is all reals except -3.}