What is the range of f(x)=1/{(x-3)(x+4)} ?

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Jim G. Share
Feb 9, 2018

Answer:

#y inRR,y!=0#

Explanation:

#f(x)=1/(x^2+x-12)" expanding factors in denominator"#

#"divide terms on numerator/denominator by the highest"#
#"power of x that is "x^2#

#f(x)=(1/x^2)/(x^2/x^2+x/x^2-12/x^2)=(1/x^2)/(1+1/x-12/x^2)#

#"as "xto+-oo,f(x)to0/(1+0-0)#

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

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

#(-oo,0)uu(0,+oo)larrcolor(blue)"in interval notation"#
graph{1/(x^2+x-12) [-10, 10, -5, 5]}

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