mathmath333
  • mathmath333
Functions
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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mathmath333
  • mathmath333
if \(\large \color{black}{\begin{align} f(x+y,x-y)=xy \hspace{1.5em}\\~\\ \end{align}}\) find \(\large \color{black}{\begin{align} f(x,y)=? \hspace{1.5em}\\~\\ \end{align}}\)
anonymous
  • anonymous
ok, have you tried it yet?
mathmath333
  • mathmath333
yes

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anonymous
  • anonymous
what did you get?
mathmath333
  • mathmath333
wait
mathmath333
  • mathmath333
i replaced x+y=a , x-y=b and got \(f(a,b)=ax-ab-yx+yb\)
anonymous
  • anonymous
very good, now eliminate a and b on the RHS
mathmath333
  • mathmath333
how do i eliminate that ?
anonymous
  • anonymous
sry eliminate x and y, well you can find x and y in terms of a and b
mathmath333
  • mathmath333
i have a question , can i just replace a and b by 'x' and 'y' \(f(a,b)=ax-ab-yx+yb\\ f(x,y)=x^2-xy-yx+y^2=(x-y)^2\)
anonymous
  • anonymous
emm no, look at to your first substitution
mathmath333
  • mathmath333
ok
mathmath333
  • mathmath333
i got x=(a+b)/2, y=(a-b)/2 is that correct substitution
anonymous
  • anonymous
that's right, put those back in the f(a,b)
mathmath333
  • mathmath333
got \(f(a,b)=\dfrac{a^2-b^2}{4}\)
anonymous
  • anonymous
we're done
mathmath333
  • mathmath333
i put now (a,b)-> (x,y) ?
anonymous
  • anonymous
yes :-)
mathmath333
  • mathmath333
oh thnx
anonymous
  • anonymous
np math

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