Q. 54.3( 10 Votes )

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

Let f : R R given by f (x) = x3.

Suppose f(x) = f(y), where x, y ϵ R.

x3 = y3 …(1)

Now, we need to show that x = y.

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

x3 ≠ y3

However, this will be contraction to (1).

Thus, x = y

Therefore, f is injective.

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