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Let f: R->Rbe defined as f(x)=x^4. Choo...

Let `f: R->R`be defined as `f(x)=x^4`. Choose the correct answer. (A) f is one-one onto (B) f is many-one onto (C) f is one-one but not onto (D) f is neither one-one nor onto

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To determine the nature of the function \( f: \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = x^4 \), we will analyze whether it is one-one (injective) and onto (surjective). ### Step 1: Check if \( f \) is one-one (injective) A function is one-one if different inputs produce different outputs. In mathematical terms, for \( f \) to be one-one, if \( f(a) = f(b) \), then it must imply that \( a = b \). Let's assume: \[ ...
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