1.
I'm trying to find the domain and range of a rational function such as
(2x+3)/(x-1)=f(x)
I know the denominator cannot be equal to zero, so the domain will be all real values except for
x=1.
For the range I thought it would be all real numbers, but the solution manual tells me that it is all
real numbers except for y=2. Can someone explain why this is so?
If this is a typo in the solution manual, then can someone explain how to find the range of
rational functions?
Solution
f(x) =2x+3/((x-1)
(x-1 ) != 0
domain is R-{1}
f'(x) = [(x-1)2 -(2x+3)1]/(x-1) 2
=-3/(x-1) 2
<0
so it is decresing fucntion
now we have to find value of f(x) when x-> 1
lim(2x+3)/(x-1)   =2    hence  this value will not be in range as x != 1
x->1
range =(-,) -{2} Â Â =R-{2}