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a fost răspuns

se considera functia f(x)=x^2-2x+2
sa se determine m apartine IR astfel incat f(m-x)=f(m+x), oricare ar fi x apartine IR

Răspuns :

Slavitescudora

f(m-x) = (m-x)² -2(m-x) + 2 = m²x-2mx+x²-2m+2x+2

f(m+x) = (m+x)² -2(m+x) +2 = m²x+2mx+x²-2m-2x+2

f(m-x) = f(m+x)

m²-2mx+x²-2m+2x+2 = m²+2mx+x²-2m-2x+2

-4mx+4x= 0

(-4m+4)x = 0

x = 0 si -4m+4 = 0

-4m = -4

m = 1