BMAD Posted May 25, 2022 Report Share Posted May 25, 2022 h(f(x)) + g(h(x)) + f(g(x)) = 2x^2 + 11x + 14 f(h(x)) + h(g(x)) + g(f(x)) = 2x^2 - 15x + 66 f(g(x)) = g(f(x)) h(g(x)) - g(h(x)) = -16x + 72 h(f(x)) + f(h(x)) = 2x^2 + 10x + 30 f(x) * g(x) = h(x) - 3x - 40 ----- f(x) = g(x) = h(x) = Quote Link to comment Share on other sites More sharing options...

0 EventHorizon Posted May 25, 2022 Report Share Posted May 25, 2022 Spoiler hf+gh+fg-fh-hg-gf = 26x - 52 hf+gh-fh-hg = 26x - 52 hf-fh = 26x - 52 - 16x + 72 = 10x + 20 2hf = 10x + 20 + 2x^2 + 10x + 30 = 2x^2 + 20x +50 -2fh = 10x + 20 - 2x^2 - 10x - 30 = -2x^2 - 10 hf = x^2 + 10x + 25 = (x+5)^2 fh = x^2 + 5 seems like... f(x) = x+5 h(x) = x^2 (x + 5) * g(x) = x^2 - 3x - 40 (x + 5) * g(x) = (x-8)*(x+5) g(x) = x-8 check... fg = x-3 = gf (x^2 + 10x + 25) + g(h(x)) + (x-3) = 2x^2 + 11x + 14 gh = 2x^2 + 11x + 14 - (x^2 + 11x + 22) = x^2 - 8 (x^2 + 5) + h(g(x)) + (x-3) = 2x^2 - 15x + 66 hg = 2x^2 - 15x + 66 - (x^2 + x + 2) = x^2 - 16x + 64 = (x-8)^2 h(g(x)) - g(h(x)) = -16x + 72 Looks like it checks out. f(x) = x+5 g(x) = x-8 h(x) = x^2 Quote Link to comment Share on other sites More sharing options...

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## BMAD

h(f(x)) + g(h(x)) + f(g(x)) = 2x^2 + 11x + 14

f(h(x)) + h(g(x)) + g(f(x)) = 2x^2 - 15x + 66

f(g(x)) = g(f(x))

h(g(x)) - g(h(x)) = -16x + 72

h(f(x)) + f(h(x)) = 2x^2 + 10x + 30

f(x) * g(x) = h(x) - 3x - 40

-----

f(x) =

g(x) =

h(x) =

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