Let #f(x) = 1/x# and #g(x) = sqrt(x-2)#, how do you find each of the compositions and domain and range?

1 Answer
Shwetank Mauria
May 17, 2018

Please see below.

Explanation:

We cannot have #x=0# in #f(x)#, hence domain is #x!=0#, which can be written in interval notation as #(-oo,0)uu(0,oo)#. As #x# varies in this domain #f(x)# can take all values except #0# andas such range too is #(-oo,0)uu(0,oo)#.

graph{1/x [-10, 10, -5, 5]}

As regards #g(x)=sqrt(x-2)#, we cannot have #x-2<0# i.e. we cannot have #x<2# and hence domain is #[2,oo)#. Given these values of #x#, #g(x)# can take values given by #g(x)>=0# and hence range is #[0,oo)#.

graph{sqrt(x-2) [-4.92, 15.08, -3.36, 6.64]}

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