Question

Se considera functia: f:R->R, f(x)=ax+b, a,b apartine R
a) demonstrati ca are loc egalitatea f(5)+f(9)=2 ori f(7) b) determinati functia f, stiind ca punctele A(0;√2) si B(√3;4√2) apartin reprezentarii grafice a functiei f

Answer 1

f(x) = ax + b 
a.
f(5)=5a + b
f(9)=9a + b
f(7)=7a + b
f(5)+f(9) = 2 * f(7)
5a + b+9a + b = 2 * (7a + b)
14a+2b=14a+2b (A)

b.
f(0)=√2 => a*0+b = √2 => b=√2
f(√3)=4√2 => √3a +b = 4√2
√3a +√2 = 4√2
√3a = 3√2
a= (3√2)√3

Functia este egala cu : $\frac{3 \sqrt{2}* x}{ \sqrt{3} } + \sqrt{2}$