Question

URGENT! 30 de puncte!

Fie f,g : R-> R, f(x) = ( m²-3m+1)x - 4, g(x)= $\frac{x}{5}-n$. Sa se determine m,n pentru care f= $g^{-1}$

Answer 1

g(x)=x/5-n
y=x/5-n
x/5=y+n
x=5y+5n
g^(-1) (x) =5x+5n=(m²-3m+1)x-4
identificam coeficientii
(m²-3m+1)=5
5n=-4

deci n=-4/5

m²-3m+1=5
m²-3m-4=0
m1=-1
m2=4


deci (m;n)∈{(-1;-4/5);(4;-4/5)}