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

Answer 1

Dom #f(x)={x in RR // x>=4}#

Range or Image of #f(x)=[0+oo)#

Since square roots of negative numbers are not real numbers, the expression under the square root must be either positive or zero.

#4-x>=0#
#4>=x#

Therefore, the set of real numbers less than or equal to four is the domain.

In interval form #(-oo,4]# or in set form
Dom #f(x)={x in RR // x>=4}#
Range or Image of #f(x)=[0+oo)#
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Answer 2

Domain: All real numbers such that ( 4 - x \geq 0 ), so ( x \leq 4 ).

Range: All real numbers such that ( f(x) \geq 0 ), so ( f(x) \geq 0 ).

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Answer 3

The domain of ( f(x) = \sqrt{4-x} ) is all real numbers ( x ) such that ( 4 - x \geq 0 ), which implies ( x \leq 4 ). Thus, the domain is ( (-\infty, 4] ).

The range of ( f(x) = \sqrt{4-x} ) depends on the domain. Since the square root function outputs only non-negative values, the range will be all non-negative real numbers up to the maximum value of the function. The maximum value occurs when ( x = 4 ), which gives ( f(4) = \sqrt{4 - 4} = \sqrt{0} = 0 ). Therefore, the range is ([0, +\infty)).

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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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