What is the domain and range of #f(x) = 1/(2x+4)#?

Answer 1

Savannah Anderson

The domain is #x in RR- {-2}#
The range is #f(x) in RR-{0}#

As we cannot divide by #0#, #x!=-2#

The domain of #f(x)# is #D_f(x)=RR-{-2}#

#lim_(x->-oo)f(x)=lim_(x->-oo)1/(2x)=0^-#

#lim_(x->+oo)f(x)=lim_(x->+oo)1/(2x)=0^+#

Consequently,

#f(x)!=0#

The range of #f(x)# is #R_f(x)=RR-{0}#

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Answer 2

Hazel Anglin

The domain of the function ( f(x) = \frac{1}{2x + 4} ) is all real numbers except ( x = -2 ) because the denominator cannot be zero.

The range of the function ( f(x) = \frac{1}{2x + 4} ) is all real numbers except ( y = 0 ) because the function will never equal zero.

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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.