If f(x)= 1 - 2x and g(x)= 3x^2 + x - 1, find all values of x satisfying f * g(x)= -5?

Question

I dont understand how to do it... Id appreciate if you can show the steps used to solve the problem so I will be able to understand similar problems.

f°g(x)... sorry i couldnt use that symbol earlier... sorry

Answer 1

I think you mean f(g(x)) and not f(x)*g(x).
f(g(x)) = 1-2(3x^2 + x - 1) = 1-6x^2-2x+2 = -6x^2-2x +3
So -6x^2-2x +3 = -5
-6x^2 - 2x +8 = 0
3x^2 +x -4 = 0
(3x +4 )(x -1) = 0
x = 1 or x -4/3

Answer 2

i assume you mean f(x)*g(x)

to answer this, multiply both functions

(1-2x)(3x^2+x-1)
=-6x^3+x^2+3x-1=-5
-6x^3+x^2+3x+4

using the factor theorem, you discover that this functions has the factors 1.13 and -0.48. Thus, these are the two possible values where f(x)g(x) eqauls -5


i guess if he meant f°g(x) i'm wrong :(