SOLUTION: 3 The function f(x) is defined as f(x) = x2 + 2x – 4. The function g(x) is defined as g(x) = –3f(x) + 2.  Graph g(x) for –2 ≤ x ≤ 2.  Describe th

Algebra ->  Equations -> SOLUTION: 3 The function f(x) is defined as f(x) = x2 + 2x – 4. The function g(x) is defined as g(x) = –3f(x) + 2.  Graph g(x) for –2 ≤ x ≤ 2.  Describe th      Log On


   



Question 828837: 3 The function f(x) is defined as f(x) = x2 + 2x – 4. The function g(x) is defined as
g(x) = –3f(x) + 2.
 Graph g(x) for –2 ≤ x ≤ 2.
 Describe the transformations that take the function f(x) onto g(x).
 Write a new function, h(x), that transforms g(x) back onto f(x).

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
g%28x%29=-3f%28x%29%2B2
g%28x%29=-3%28x%5E2%2B2x-4%29%2B2 ------ because g is composed of f, so substituted
g%28x%29=-3x%5E2-6x%2B12%2B12
highlight%28g%28x%29=-3x%5E2-6x%2B14%29
Graph that if you want. Might be better to put into standard for to know if opens up or down, and where is vertex, intercepts.

Then you wanted f(x) composed of g(x).
Starting with f(x) definition,
f%28x%29=x%5E2%2B2x-4
'
h%28x%29=f%28g%28x%29%29=%28-3x%5E2-6x%2B14%29%5E2%2B2%28-3x%5E2-6x%2B14%29-4
9x%5E4%2B36x%5E3-48x%5E2-168x%2B196-6x%5E2-12x%2B28-4
highlight%28h%28x%29=9x%5E4%2B36x%5E3-54x%5E2-180x%2B220%29
Lengthy process to try to break that into factors, if it can be done.

g(x)..... graph
graph%28300%2C300%2C+-2%2C2%2C-5%2C20%2C-3x%5E2-6x%2B14%29