How do you find the range of $x + sqrt( x-1 )$ ?

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Answer 1 · 2015-09-18T14:47:38

The range is $[1,+oo)$

Set $f(x)=x+sqrt(x-1)$ this is defined for $x-1>=0=>x>=1$ .Hence
the domain is $[1,+oo)$

Hence the minimum value for f(x) is at x=1 then f(1)=1 and the range is

$[f(1),+oo)=[1,+oo)$

How do you find the range of x + sqrt( x-1 )x + sqrt( x-1 )?