can someone help me with this question?

let z = F(x, y) = x^2 -y +1

b)find the functions g(x,y)= f( f(x,y) , y) and h(x,y)= f(x, (f(x,y) )

c)If f(x,y)= f(y,x) and x cannot equal to y

show that y= -x -1

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- Mar 2nd 2009, 05:31 PMKQ_jaii dont understand the notations.
can someone help me with this question?

let z = F(x, y) = x^2 -y +1

b)find the functions g(x,y)= f( f(x,y) , y) and h(x,y)= f(x, (f(x,y) )

c)If f(x,y)= f(y,x) and x cannot equal to y

show that y= -x -1 - Mar 2nd 2009, 06:07 PMronaldo_07
- Mar 2nd 2009, 06:25 PMarpitagarwal82
a

f( f(x,y) , y)

= $\displaystyle (x^2 -y +1)^2 -y +1$

b

f(x,y)= f(y,x)

$\displaystyle => x^2 -y +1 = y^2 -x +1$

$\displaystyle = >x^2 - y^2 = y - x$

$\displaystyle => (x - y)(x + y) = y - x$

since x - y is not equal to zero, we can divide equation by x - y

$\displaystyle => x + y = -1$

$\displaystyle => y= -x -1 $