find the range

Question

How do I find the range of

 

f(x)=x+4

        x+2

 

I know that to find the domain I need to set the denominator =0 and solve. But i'm not sure what to do to find the range.

Answer 1

I believe that you're intending to deal with the rational algebraic function f(x) = (x+4) / (x+2)

 

which has Domain all Reals except -2.

 

This function has an inverse, and its Range is ALL REALS EXCEPT -2 by virtue of the interchange of variables that is used to derive f^-1.

 

I find f^-1(x) = -2(x+1) / (x-1) and its domain is all Reals except 1.

 

THEREFORE THE RANGE OF f IS ALL REALS EXCEPT 1.

 

You can verify this by attempting to set f(x) = 1; that equation has no solution.