Q. 54.3( 10 Votes )

# Show that the function f : R → R given by f (x) = x^{3} is injective.

Answer :

Let f : R → R given by f (x) = x^{3}.

Suppose f(x) = f(y), where x, y ϵ R.

⇒ x^{3} = y^{3} …(1)

Now, we need to show that x = y.

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

⇒ x^{3} ≠ y^{3}

However, this will be contraction to (1).

Thus, x = y

Therefore, f is injective.

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