Question

How to solve (only hints, not answer): f(x) = ax+b, g(x) = cx^2. Determine for which constants a,b, and c it is true that f(g(x)) = g(f(x))
I get the composition, but I don't know how to simplify from what I get.
f of g = a(cx^2) + b = acx^2 +b
g of f = c(ax+b)^2
So I want to find when this is true: acx^2 + b = c(ax+b)^2

Answer 1

okay i hate precalculus, so i can't help you, but i'm sure you can find an online calculator that will explain the steps it went through

Answer 2

Fiven f(x) and g(x), what is f(g(x)) and what is g(f(x))?

Answer 3

Given*

Answer 4

up to here is correct:
acx^2 + b = c(ax+b)^2

The next step I would do is expand the (ax+b)^2

Answer 5

@ninjalobster

Answer 6

okay, so then I have
acx^2 + b = c(a^2x^2 + 2abx + b^2)
Distributing the c:
acx^2 + b = (c)a^2x^2 + 2abcx + (c)b^2
I'm pretty sure that I am not looking for actual decimal values, should I just solve for each constant individually?

Answer 7

mmm.. i'm not sure if i'd solve for each constant,
i'd try to simplify and eliminate as many terms as I can from the two sides now, so get all the terms that have the same variable on one side, and see if you can factor out a common variable in each term and see if you can get that same variable factored out of the other side aswell, and start canceling out variables.