The function f is defined by f:x =6x-x^2-5 Find set of values of x for which f(x)<3 I have done finding x values that are 2 and 4 But I don't know which direction inequality sign should be?

1 Answer
Jim G.
May 3, 2018

#x< 2" or "x>4#

Explanation:

#"require "f(x)<3#

#"express "f(x)<0#

#rArr-x^2+6x-5<3#

#rArr-x^2+6x-8<0larrcolor(blue)"factor the quadratic"#

#rArr-(x^2-6x+8)<0#

#"the factors of + 8 which sum to - 6 are - 2 and - 4"#

#rArr-(x-2)(x-4)<0#

#"solve "(x-2)(x-4)=0#

#x-2=0rArrx=2#

#x-4=0rArrx=4#

#rArrx=2,x=4larrcolor(blue)"are the x-intercepts"#

#"the coefficient of the "x^2" term "<0rArrnnn#

#rArrx<2" or "x>4#

#x in(-oo,2)uu(4,oo)larrcolor(blue)"in interval notation"#
graph{-x^2+6x-8 [-10, 10, -5, 5]}

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