(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that f is a differentiable function of a single variable and F(x,y) is defined by F(x,y) = f(x^2 - y)

Problem: Given that F(0,y) = sin y for all y, find a formula for F(x,y)

2. Relevant equations

3. The attempt at a solution

This is what the tutor had put up on the board, but I couldn't make any sense of it:

F(0,y) = sin y

F(0,y) = f(-y) = sin y = sin (-(-y))

F(x,y) = sin (-(x^2-y)) = sin(y-x^2)

I understand that he got f(-y), and given the equation at the start that it results in sin y, but I do not understand how he got sin (-(-y)) and onwards.

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# Homework Help: Finding a formula from a single variable differentiable function

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