aplicacions lineals

f(x,y) = 2x+4y

f(a+b,c+d) = 2·(a+b)+4·(c+d) = (2a+4c)+(2b+4d) = f(a,c)+f(b,d)

2x+4y = 0 <==> x = (-2)·y

f(x,y) = x^{2}·y^{4}

f(a·b,c·d) = (a·b)^{2}·(c·d)^{4} = (a^{2}·c^{4})·(b^{2}·d^{4}) = f(a,c)·f(b,d)

x^{2}·y^{4} = 1 <==> x = y^{(-2)}

f(x,y) = 3x+y

f(a+b,c+d) = 3·(a+b)+(c+d) = (3a+c)+(3b+d) = f(a,c)+f(b,d)

3x+y = 0 <==> x = (-1)·(1/3)·y

f(x,y) = x^{3}·y

f(a·b,c·d) = (a·b)^{3}·(c·d) = (a^{3}·c)·(b^{3}·d) = f(a,c)·f(b,d)

x^{3}·y = 1 <==> x = y^{(-1)·(1/3)}

f(x,y) = mx+ny

f(a+b,c+d) = m·(a+b)+n·(c+d) = (ma+nc)+(mb+nd) = f(a,c)+f(b,d)

mx+ny = 0 <==> x = (-1)·(n/m)·y

f(x,y) = x^{m}·y^{n}

f(a·b,c·d) = (a·b)^{m}·(c·d)^{n} = (a^{m}·c^{n})·(b^{m}·d^{n}) = f(a,c)·f(b,d)

x^{m}·y^{n} = 1 <==> x = y^{(-1)·(n/m)}