Given #f(x)=sqrtx# and #g(x)=x-1#, how do you determine the domain and range of #y=f(g(x))#?

1 Answer
Binayaka C.
Jun 20, 2017

Domain : #x>=1#. In interval notation #[1,oo)#
Range: #y>=0 #. In interval notation #[0,oo)#

Explanation:

#f(x)=sqrtx ; g(x)=x-1 ; y=f(g(x))= ?#

Here Inside function is #g(x)=x-1#. Domain of inside function is any real number #x in RR# , Range: #g(x) in RR#

#y=f(g(x)) = f(x-1) = sqrt(x-1)# . Domain: under root should be #>=0 :. x-1>=0 or x>=1#.

Domain :#x>=1#.In interval notation #[1,oo)#

Range: #y>=0 # In interval notation #[0,oo)#
graph{sqrt(x-1) [-10, 10, -5, 5]} [Ans]

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