# i dont understand the notations.

• Mar 2nd 2009, 05:31 PM
KQ_jai
i 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 PM
ronaldo_07
Quote:

Originally Posted by KQ_jai
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

I think it means that for g(x,y) you put x^2 -y +1 in to x
and for h(x,y) you put x^2 -y +1 into the y
• Mar 2nd 2009, 06:25 PM
arpitagarwal82
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 \$