List all x-value(s) of ordered pairs of the form (x,1) that are on the rational function f(x)=(6-2x)/((x-3)(x+5))f(x)=6−2x(x−3)(x+5)?
1 Answer
Nov 9, 2017
Explanation:
"note that "x!=3,-5" as this would make "f(x)note that x≠3,−5 as this would make f(x)
"undefined"undefined
"factorising the numerator"factorising the numerator
f(x)=(-2(x-3))/((x-3)(x+5))f(x)=−2(x−3)(x−3)(x+5)
color(white)(f(x))=(-2cancel((x-3)))/(cancel((x-3))(x+5))=(-2)/(x+5)
"the cancelling of the factor "(x-3)" indicates a hole at x = 3"
"solve "(-2)/(x+5)=1
rArrx+5=-2
rArrx=-7
"hence the only point on "f(x)" is "(-7,1)
graph{(6-2x)/((x-3)(x+5)) [-10, 10, -5, 5]}
