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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