Question

Functions

Answer 1

if

\(\large \color{black}{\begin{align} f(x+y,x-y)=xy \hspace{1.5em}\\~\\
\end{align}}\)

find


\(\large \color{black}{\begin{align} f(x,y)=? \hspace{1.5em}\\~\\
\end{align}}\)

Answer 2

ok, have you tried it yet?

Answer 3

yes

Answer 4

what did you get?

Answer 5

wait

Answer 6

i replaced x+y=a , x-y=b

and got

\(f(a,b)=ax-ab-yx+yb\)

Answer 7

very good, now eliminate a and b on the RHS

Answer 8

how do i eliminate that ?

Answer 9

sry eliminate x and y, well you can find x and y in terms of a and b

Answer 10

i have a question , can i just replace a and b by 'x' and 'y'

\(f(a,b)=ax-ab-yx+yb\\
f(x,y)=x^2-xy-yx+y^2=(x-y)^2\)

Answer 11

emm no, look at to your first substitution

Answer 12

ok

Answer 13

i got x=(a+b)/2, y=(a-b)/2 is that correct substitution

Answer 14

that's right, put those back in the f(a,b)

Answer 15

got

\(f(a,b)=\dfrac{a^2-b^2}{4}\)

Answer 16

we're done

Answer 17

i put now (a,b)-> (x,y) ?

Answer 18

yes :-)

Answer 19

oh thnx

Answer 20

np math