How do you find the domain and range of #f(x) = sqrt(x-4) +6#?

Answer 1

The domain is #x in [4, +oo[#
The range is #f(x) in [6,+oo[#

What is under the #sqrt# sign is #>=0#
#x-4>=0#
#x>=4#
The domain of #f(x)# is #D_f(x)= [4, +oo[#
When #x=4#, #f(4)=6#
#lim_(x->+o)f(x)=+oo#
The range is #R_f(x)=[6,+oo[#
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Answer 2

The domain of the function ( f(x) = \sqrt{x-4} + 6 ) is all real numbers greater than or equal to 4, denoted as ( x \geq 4 ), since the expression inside the square root must be non-negative.

The range of the function ( f(x) = \sqrt{x-4} + 6 ) is all real numbers greater than or equal to 6, denoted as ( f(x) \geq 6 ), because the square root function always produces non-negative values, and adding 6 to non-negative values will result in values greater than or equal to 6.

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Answer 3

To find the domain and range of ( f(x) = \sqrt{x-4} +6 ):

  1. Domain: Set the expression inside the square root, ( x-4 ), greater than or equal to zero and solve for ( x ). [ x - 4 \geq 0 ] [ x \geq 4 ] So, the domain is all real numbers greater than or equal to 4.

  2. Range: The square root function always returns non-negative values.

    • The minimum value of ( \sqrt{x-4} ) is 0 when ( x = 4 ).
    • Adding 6 to this minimum value gives us the minimum value of the function. Therefore, the range is all real numbers greater than or equal to 6.
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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.

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.

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.

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.

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