How do you find the domain and range of #y=(2x)/(-x-5)#?

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Answer 1 · 2017-02-14T10:59:40

The domain of #y# is #RR-{-5}#
The range of #y# is #RR-{-2}#

As you cannot divide by #0#, #-x-5!=0#

The domain of #y# is #D_y=RR-{-5}#

To find the range, we need #f^-1(x)#

#y=2x/-x-5#

#-yx-5y=2x#

#2x+yx=-5y#

#x(y+2)=-5y#

#x=(-5y)/(y+2)#

Therefore,

#f^-1(x)=(-5x)/(x+2)#

The range of #f(x)# is the domain of #f^-1(x)#

The range of #f(x)# is #R_y=RR-{-2}#