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If f(x)= 3x+5 and h(x)= 3x^2 +3x+2, find a function g such that f o g=h .
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`f(x) = 3x+5`
`h(x) = 3x^2 +3x+2`
In `f_og` the term x in function f(x) is replace by g(x).
`f_0g = 3g(X)+5`
`f_0g = h(x)`
`3g(x)+5 = 3x^2 +3x+2`
`3g(x) =3x^2 +3x-3 `
`g(x) = x^2+x-1`
So the function `g(x) = x^2+x-1`
Posted by jeew-m on October 2, 2012 at 12:23 AM (Answer #1)
High School Teacher
Just by trial and error, it can be seen that if `g(x)=x^2+x-1`, then
` ` so that's the answer. There is a way to do it without having to guess, though. Note that if we have
`f@g=h,` then `g=(f^(-1)@f)@g=f^(-1)@(f@g)=f^(-1)@h.`
So either way we do it, we get `g(x)=x^2+x-1.`
Posted by degeneratecircle on October 2, 2012 at 12:24 AM (Answer #2)
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