1 Given fx x2x2 and gx x22x2 A Solve fx gx B Solve fx gx

1:

Given f(x) = x^2-x-2 and g(x) = -x^2+2x-2;

A. Solve f(x) > g(x)

B. Solve f(x) <= 0

4:

Given h(x) = (2x^3 - 2x^2) - (56x+56)

A. Find all the zeros.

5:

Given f(x) = x^4+6x^3-24x-16;

A. Find all zeros

6:

Given g(x)=x^3-1/2x^2-12x+6;

A. Find all zeros.

can someone help me see what I did wrong and how to solve this? It is for practice questions for an exam that I need to know how to do to get ready for the exam.

Solution

Given f(x) = x^2-x-2 and g(x) = -x^2+2x-2;

A. Solve f(x) > g(x)

x^2 -x -2 > -x^2 +2x -2

2x^2 -3x >0

x(2x -3) >0

Solution x< 0 or x> 3/2

(-infinty , 0) U ( 3/2 , inf)

B. Solve f(x) <= 0

x^2-x-2 <=0

(x+1)(x-2) <=0

x-2< 0 for x<2

x-2> 0 for x>2

x+1< 0 for x< -1

x+1>0 for x>-1

So, solution for x^2-x-2 <=0

-1<=x<=2

[-1 , 2]