If g(x) = 3x + 2 and h(x) = 9x2 + 12x + 6, find a function f such that f ○ g = h

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22-12-2017
Mathematics

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If g(x) = 3x + 2 and h(x) = 9x2 + 12x + 6, find a function f such that f ○ g = h

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altavistard altavistard · Answer 1 · 2017-12-26T04:57:54+01:00

altavistard altavistard

26-12-2017

f(g(x)) = f(3x+2) = h(x)=9x^2+12x + 6

Note that (3x+2)^2 = 9x^2 + 12x + 4, which is almost, but not quite, equal to h(x).

Let's experiment. What if f(x) = x^2 + 2?

Then f(3x+2) = (3x+2)^2 + 2 = 9x^2 + 12x + 4 + 2 = 9x^2 + 12x + 6, which is the same as the given h(x).

Thus, f(x) is x^2 + 2.

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