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How do you find the domain and range of #f(x) = 5/(x-9)#?

Answer 1

#x inRR,x!=9#
#y inRR,y!=0#

The value that x cannot be is obtained by equating the denominator to zero and solving the function; otherwise, f(x) would become undefined.

#"solve "x=9=0rArrx=9larrcolor(red)"excluded value"#

#rArr"domain is "x inRR,x!=9#

#"for the range rearrange making x the subject"#

#y=5/(x-9)#

#"multiply both sides by "(x-9)#

#rArry(x-9)=5#

#rArrxy-9y=5#

#rArrxy=5+9y#

#rArrx=(5+9y)/y#

#"the denominator cannot equal zero"#

#rArry=0larrcolor(red)"excluded value"#

#rArr"range is "y inRR,y!=0#

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Answer 2

Jace Anderson

To find the domain of ( f(x) = \frac{5}{x - 9} ), set the denominator ( x - 9 ) not equal to zero and solve for ( x ): [ x - 9 \neq 0 ] [ x \neq 9 ]

So, the domain of ( f(x) ) is all real numbers except ( x = 9 ).

To find the range, note that the function is a rational function. Since the denominator can approach zero as ( x ) approaches 9, the function can take on arbitrarily large positive or negative values. Therefore, the range of ( f(x) ) is all real numbers except ( 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.