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
May 3, 2018
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]}