Mathematics

Mathematics

Problem

a. Part 1: Let f:R→Rf:\text{ℝ}\to\text{ℝ} be defined by f(x)=x3−3x+1f(x)=x^{3}-3x+1. Solve the equation f(x1)=f(x2)f(x_{1})=f(x_{2}) for x1,x2∈Rx_{1},x_{2}\in\text{ℝ}. Hence decide whether ff is injective on R\text{ℝ}. a. Part 1: Let f:R→Rf:\text{ℝ}\to\text{ℝ} be defined by f(x)=x3−3x+1f(x)=x^{3}-3x+1. Solve the equation f(x1)=f(x2)f(x_{1})=f(x_{2}) for x1,x2∈Rx_{1},x_{2}\in\text{ℝ}. Hence decide whether ff is injective on R\text{ℝ}.

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