What is the domain and range of #g(x)=2/(x+5)#?

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Answer 1 · 2017-02-25T14:29:30

The domain of #g(x)# is #D_g(x)=RR-{-5}#
The range of #g(x)# is #R_g(x)=RR-{0}#

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

The domain of #g(x)# is #D_g(x)=RR-{-5}#

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

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

#(x+5)y=2#

#xy+5y=2#

#xy=2-5y#

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

Therefore,

#g^-1(x)=(2-5x)/x#

The domain of #g^-1(x)=RR-{0}#

This is the range of #g(x)#

The range of #g(x)# is #R_g(x)=RR-{0}#