What is the domain and range of #f(x)= sqrt(x-4) + 2#?

1 Answer
iceman
Oct 29, 2015

The domain is: #x>=4#
The range is: #y>=2#

Explanation:

The domain is all the x values where a function is defined. In this case the given function is defined as long as the value under the square root sign is greater than or equal to zero, thus:
#f(x)=sqrt(x-4)+2#
The domain:
#x-4>=0#
#x>=4#
In interval form:
#[4,oo)#
The range is the all the values of a function within its valid domain, in this case the minimum value for x is 4 which makes the square root part zero, thus:
The range:
#y>=2#
In interval form:
#[2,oo)#

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