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Check the nature of the function f(x)=x...

Check the nature of the function ` f(x)=x^(3)+x+1, x in R ` using analytical method and differentiation method.

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To check the nature of the function \( f(x) = x^3 + x + 1 \) analytically and using differentiation, we will follow these steps: ### Step 1: Check if the function is one-to-one (1-1) To determine if the function is one-to-one, we need to check if \( f(x_1) = f(x_2) \) implies \( x_1 = x_2 \). Assume: \[ ...
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