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  4. The function f:R→ R given by f(x)=x3-1 is

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Q. The function $ f:R\to R $ given by $ f(x)={{x}^{3}}-1 $ is

J & K CETJ & K CET 2008Relations and Functions - Part 2

Solution:

Given, $ f(x)=\,{{x}^{3}}-1 $
Let $ {{x}_{1}}\,,\,{{x}_{2}}\,\in \,R. $
Now, $ f({{x}_{1}})=f({{x}_{2}}) $
$ \Rightarrow $ $ x_{1}^{3}-1=x_{2}^{3}-1 $
$ \Rightarrow $ $ x_{1}^{3}=x_{2}^{3}\,\,\,\Rightarrow \,\,\,{{x}_{1}}={{x}_{2}} $
$ \therefore $ $ f(x) $ is one-one. Also, it is onto. Hence, it is a bisection.