Q.5 Show that the function f : R \rightarrow R given by f (x) = x ^3 is injective.

Answers (1)

f : R \rightarrow R

f (x) = x ^3

One-one:

   Let    f(x)=f(y)\, \, \, \, \, \, x,y \in R

             x^{3}=y^{3}

We need to prove x=y.So,

  • Let    x\neq y then there cubes will not be equal i.e. x^{3}\neq y^{3}.
  •  It will contradict given condition of cubes being equal. 
  • Hence, x=y  and it is one -one which means it is injective.
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