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

Answer 1

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

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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Answer 2

Jace Anderson

Domain: (x \geq 4) Range: (f(x) \geq 2)

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.