Math Problem (easy??)
f(g(x))=4x²-8x+3
f(x)= x²-2x
what was g(x)?
#math #iForgor
https://sauropods.win/@futurebird/113511919517150285
@futurebird I’m not sure how “easy” but it was fun to figure out even if it meant unburying things long forgotten.
Thanks for sharing!
@futurebird
I found it easy, but for a high school student without a particular interest in Math, it might be really tricky.
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2024-11-19 neuronoise ┃ edited
@futurebird Also, the fact that solutions exist at all is a lucky coincidence. I believe that of you replace the right-hand side of your initial equation by something like -x²+2x-2 you find […]
@futurebird hi! Not sure this is of interest, but in this case there are two possible solutions g, because the function f is not invertible. One can find the two right inverses of f solving […]
@futurebird It makes sense that g should be linear, with g(x)=mx+b. The quadratic coefficient of 4 in f(g(x)) would necessitate m=±2. Let's look at m=2 first; then […]
[guess]
@futurebird
Let's see: in order to have a solution, g needs to be linear, i.e. g(x) = ax + b
Substituting, we get:
f(g(x)) = a²x² + 2abx + b² - 2ax - 2b = a²*x² + (2ab - 2a)*x - 2b + […]
@futurebird hah?
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