#### Question

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

#### Solution

*f*: **R** → **R** is given as *f*(*x*) = *x*^{3}.

Suppose *f*(*x*) = *f*(*y*), where *x*, *y* ∈ **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 a contradiction to (1).

∴ *x* = *y*

Hence, *f* is injective.

Is there an error in this question or solution?

Solution Show that the Function F: R → R Given by F(X) = X3 is Injective. Concept: Types of Functions.