Question 266599
Here is the original equation
(i) {{{f(x)=(x-2)/(x+3)}}}
to find the inverse switch the x and y parts.
(ii) {{{x = (y-2)/(y+3)}}}
cross multiply to get
(iii) {{{xy + 3x = y-2}}}
add 2 and then subtract xy to get
(iv) {{{ 3x+2 = y - xy}}}
factor out the y to get
 (v) {{{3x +2 = y(1-x)}}}
divide by 1-x to get
(vi) {{{((3x+2)/(1-x)) = y^-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