SOLUTION: show that f(x)=(x-2)/(x+3) is invertible by finding its inverse. (a) what is the domain of f(x)? the range of f-1(x)? (b) what is the domain of f-(x)? the range of f(x)?

Question 266599: show that f(x)=(x-2)/(x+3) is invertible by finding its inverse.
(a) what is the domain of f(x)? the range of f-1(x)?
(b) what is the domain of f-(x)? the range of f(x)?
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
Here is the original equation
(i)
to find the inverse switch the x and y parts.
(ii)
cross multiply to get
(iii)
add 2 and then subtract xy to get
(iv)
factor out the y to get
(v)
divide by 1-x to get
(vi)
this is the inverse
----
a). domain of f(x) is all reals except x = -3
The range of f^(-1)(x) is all reals except y = -3
b). The range of f(x) is all reals except y = 1
the domain of f^(-1)(x) is all reals except x = 1
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