Let F(x, y) = f(y − x + g(y + x)), where f(u) and g(u) are suﬃciently(adsbygoogle = window.adsbygoogle || []).push({});

diﬀerentiable functions of a single real variable. If, in a neighbourhood of

(x, y) = (a, b), the equation F(x, y) = 0 deﬁnes a function y(x), state the

condition(s) on f and g so that y′(x) exists in a neighbourhood of x = a.

2. Relevant equations

I've done all that maths part after this question, but I'm not sure how to define it. It uses the implicit function theorem.

3. The attempt at a solution

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# Homework Help: Implicit Function Theorem

Can you offer guidance or do you also need help?

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