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Let f: RvecR be a function satisfying co...

Let `f: RvecR` be a function satisfying condition `f(x+y^3)=f(x)+[f(y)]^3fora l lx ,y in Rdot` If `f^(prime)(0)geq0,` find `f(10)dot`

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To solve the problem, we need to analyze the functional equation given and derive the possible forms of the function \( f(x) \). ### Step-by-Step Solution: 1. **Given Functional Equation**: \[ f(x + y^3) = f(x) + [f(y)]^3 \quad \forall x, y \in \mathbb{R} \] ...
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