Question: Please try to include all steps in the answer. Thanks in advance. Nothing is missing in these question. 4. If S is a smooth surface,

Please try to include all steps in the answer. Thanks in advance. Nothing is missing in these question.

4. If S is a smooth surface, define the notion of a smooth function S -> R. Show that, if S is a smooth surface, each component of the inclusion map S - R' is a smooth function S => R. 5. Show that translations and invertible linear transformations of R3 take smooth surfaces to smooth surfaces

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