(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the function g(x), if there are [itex]h=g \circ f[/itex]

f(x)=x+1, [itex]x \in \mathbb{R}[/itex] and [itex]h(x)=x^3+3x+1[/itex]

2. Relevant equations

[tex](g \circ f)(x)=g(f(x))=h(x)[/tex]

[tex]f \circ g \neq g \circ f [/tex]

3. The attempt at a solution

[tex]h=g \circ f[/tex]

[tex]h(x)=g(f(x))[/tex]

[tex]x^3+3x+1=g(x+1)[/tex]

Is there any way that I will directly find the result of g(x), or I should guess and try some things? I tried something at home, but useless. Please help me!

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# Composition and polynomial

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