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)?

Algebra ->  Trigonometry-basics -> 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)?      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the original equation
(i) f%28x%29=%28x-2%29%2F%28x%2B3%29
to find the inverse switch the x and y parts.
(ii) x+=+%28y-2%29%2F%28y%2B3%29
cross multiply to get
(iii) xy+%2B+3x+=+y-2
add 2 and then subtract xy to get
(iv) +3x%2B2+=+y+-+xy
factor out the y to get
(v) 3x+%2B2+=+y%281-x%29
divide by 1-x to get
(vi) %28%283x%2B2%29%2F%281-x%29%29+=+y%5E-1
this is the inverse
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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