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?

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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?

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Answer 1 · 2018-05-03T14:54:52

$x< 2" or "x>4$

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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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

Explanation:

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