About function

Real Analysis
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Tolaso J Kos
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About function

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Post by Tolaso J Kos »

Let \( f:\mathbb{R} \longrightarrow \mathbb{R} \) defined by \( f(x)=\left\{\begin{matrix}
x^2 \, , \, &x \in \mathbb{R}\setminus \mathbb{Q} \\
x^3 \, , \, &x \in \mathbb{Q}
\end{matrix}\right. \)

a. Is \( f \) \( 1-1 \) ?

b. Determine the points at which the function is continuous.

c. Evaluate the derivative at the points at which the function is differentiable.
Imagination is much more important than knowledge.
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