(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Finding a formula from a single variable differentiable function

**Physics Forums | Science Articles, Homework Help, Discussion**