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secondary 4 | E Maths
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For now, my g(f(x)) = x^2 - 6x + 9. I need help to form a relationship between hgf(x) and g(f(x)) to get function h.
Date Posted: 3 years ago
Views: 187
Actually, do you realise that you're very close already?
f(x) = x - 3, g(x) = x²
gf(x) = (x - 3)² = x² - 6x + 9
You just need to continue from here by expressing hgf(x) in terms of gf(x).
You're basically substituting gf(x) in as your independent variable.
hgf(x)
= x² - 6x + 3
= x² - 6x + 9 - 6
= gf(x) - 6
So, it is simply h(x) = x - 6
gf(x) = (x - 3)² = x² - 6x + 9
You just need to continue from here by expressing hgf(x) in terms of gf(x).
You're basically substituting gf(x) in as your independent variable.
hgf(x)
= x² - 6x + 3
= x² - 6x + 9 - 6
= gf(x) - 6
So, it is simply h(x) = x - 6
If this is not clear, try seeing gf(x) as X
(i.e let X = gf(x) = x² - 6x + 9)
h(X)
= X - 6
= x² - 6x + 9 - 6
= x² - 6x + 3
= hgf(x)
(i.e let X = gf(x) = x² - 6x + 9)
h(X)
= X - 6
= x² - 6x + 9 - 6
= x² - 6x + 3
= hgf(x)
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