find all the values of x satisfying the given conditions.

Question

f(x)=1-2x

2(x)=3x²+x-1

(fοg)(x)=-5

Answer 1

Let f(x)=1-2x

     g(x)=3x²+x-1

 

Then, (fog)(x)=f(g(x))=1-2(3x²+x-1) (substitute the g function into the f function)

                                 =1-6x²-2x+2

                                 =-6x²-2x+3

Since (fog)(x)= -5, we get:

-5=-6x²-2x+3

+5            +5

0 =-6x²-2x+8

 

0 = -2(3x²+x-4)

0 = -2(3x+4)(x-1)

 

x=-4/3 or x=1

 

Checking x=1 into original (fog)(x)=-5 equation above:

-5=-6(1)²-2(1)+3

-5=-6-2+3

-5=-5

 

Checking x=-4/3:

-5=-6(-4/3)² -2(-4/3)+3

-5=-5

 

Answer:{-4/3,1}

 

 

 

{-4/3,1}  set notation

{x: x=-4/3 or x=1} set builder notation