How do you find the domain and range of #f(x)=(2x-1)/(3-x)#?
2 Answers
Perform polynomial division on
Explanation:
For a rational function of the form
From this it is evident that this is a rectangular hyperbola with asymptotes at
Therefore we get,
Explanation:
#"f(x) is defined for all real values of x apart from values that "#
#"make the denominator zero"#
#"Equating the denominator to zero and solving gives the value"#
#"that x cannot be"#
#"solve " 3-x=0rArrx=3larrcolor(red)" excluded value"#
#rArr"domain is "x inRR,x!=3#
#"to find any excluded values in the range rearrange y = f(x)"#
#"making x the subject"#
#rArry(3-x)=2x-1#
#rArr3y-xy=2x-1#
#rArr-xy-2x=-(1+3y)#
#rArrx(-y-2)=-(1+3y)#
#rArrx=-(1+3y)/(-y-2)#
#"the denominator cannot equal zero"#
#"solve " -y-2=0rArry=-2larrcolor(red)"excluded value"#
#rArr"range is " y inRR,y!=-2#