Answer:
[tex](f+g)(x)= 5x^3-2x^2-5x+8[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=x^3-2x^2+1\\g(x)=4x^3-5x+7\end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
The composite function (f + g)(x) means to add function f(x) and g(x):
[tex]\begin{aligned}(f+g)(x) & = f(x)+g(x)\\& = (x^3-2x^2+1)+(4x^3-5x+7)\\& = x^3-2x^2+1+4x^3-5x+7\\& = x^3+4x^3-2x^2-5x+1+7\\& = 5x^3-2x^2-5x+8 \end{aligned}[/tex]
Learn more about composite functions here:
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