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Studentc14
Functions! Please help, very important! :) (file attached)
f . g = h f = 3x + 5 h = 3x^2 + 3x + 2 so f(g(x)) = 3x^2 + 3x + 2 That means: 3(g(x)) + 5 = 3x^2 + 3x + 2 By inspection: g(x) = x^2 + x - 1
what's inspection, sorry?
Figuring it out by looking at it
I don't follow, how you get this part? 3(g(x)) + 5 = 3x^2 + 3x + 2
we know h(x) = 3x^2 + 3x +2 --------> (1) and we know f.g = f(g(x)) but f(x) = 3x + 5, therefore f(g(x)) = 3(g(x)) + 5 --------> (2) and we know that f.g = h ----> f(g(x)) = h(x) therefore: (1) = (2) 3(g(x)) + 5 = 3x^2 + 3x +2
ohkay, and then you can kinda just look at it and like guess and check and see that x^2+x-1 works for g, right?
Yes. Or you can just solve G like a normal variable: 3(g(x)) + 5 = 3x^2 + 3x +2 Substract 5 on both sides: 3(g(x)) = 3x^2 + 3x -3 Divide by 3: g(x) = x^2 + x - 1
oh! that's much clearer. thank you so much!
haha, colloquial for "cool, no problem"