Exercise · ZW-SMOOTH-FUNCTION-007 · ★★☆ Intermediate
If \(f\) and \(g\) from \(\mathbb{R}\) to \(\mathbb{R}\) are smooth, what can be said about \(g\circ f\)?
Choose one option.
Show answer
- D. It is smooth
Explanation
The composition of smooth functions is smooth, by repeatedly applying the chain rule.
Review the concept: Smooth function
A smooth function is a function between spaces with differentiable structure that, written in local coordinates, has derivatives of all orders.
\[f\in C^{\infty}(M,N)\]
More practice problems: smooth function
- ZW-SMOOTH-FUNCTION-001 What does it mean for f to be of class C^∞?
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- ZW-SMOOTH-FUNCTION-008 Let f(x)=x^2sin (1/x) for xne 0 and f(0)=0. Which statement is correct?
- ZW-SMOOTH-FUNCTION-009 What is a diffeomorphism between two smooth manifolds?