show that the function ` f : R to R f : (x) = x^(5)` is one-one and onto .

Explanation

To show that the function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = x^5 \) is one-one and onto, we will proceed with the following steps:

### Step 1: Show that \( f \) is one-one (injective)

To prove that \( f \) is one-one, we need to show that if \( f(x_1) = f(x_2) \), then \( x_1 = x_2 \).

1. Assume \( f(x_1) = f(x_2) \).
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