Question

Show that the function $f:R\to R$ given by $f(x)=x^3$ is injective.

Answer 1

f: R $\to$ R is given as $f(x)=x^3.$
Suppose f(x) = f(y), where x, y ∈ R. $\Rightarrow$ 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 a contradiction to (1).
∴ x = y
Hence, f is injective.