1.

Show that the function f :R → R given by f (x) = x3 is injective.

Answer»

Here, f :R→R is given as f(x) = x3. 

Suppose, f(x) = f(y),where x,y ∈ R ⇒ x3 = y3 …(i) 

Now, we need to show that x = y 

Suppose, x ≠ y, their cubes will also not be equal. x3 ≠ y3

However, this will be a contradiction to Eq. i). 

Therefore, x = y. Hence, f is injective.


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