How do you find the domain and range of # f(x) = (x+6 )/ (2x+1 )#?

Answer 1

#f:RR rarr RR, x != -1/2#

To find which values of #x# don't belong to the domain of #f#, we have to set the denominator of #f=0# and solve for #x#
#2x+1=0#
#x=-1/2#
Therefore, #-1/2# is the only invalid real in the domain. Also, since #x=-1/2# is an asymptote, we know that #f# will increase with bound towards #+-oo#. Therefore, #f# maps to all #y in RR#.

Putting these two together, we can define

#f:RR rarr RR#
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Answer 2

To find the domain of the function ( f(x) = \frac{x + 6}{2x + 1} ), we need to consider the values of ( x ) for which the denominator ( 2x + 1 ) is not equal to zero. So, the domain is all real numbers except for the value that makes the denominator zero. Therefore, the domain is ( x \neq -\frac{1}{2} ).

To find the range of the function, we need to determine the possible output values of ( f(x) ). Since the function is a rational function, the range will be all real numbers except for the values that would cause the function to be undefined. So, the range is all real numbers except for the value that makes the denominator zero, which is ( f(x) \neq 0 ).

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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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