Question

3. Fie funcţia f:R→R, f(x) = 5-x. Să se calculeze: a) ƒ(1)+ ƒ(2)+...+ f(100); b) f(1)*f(2)*....*f(100).​

Answer 1

Răspuns:

a) -4550; b) 0

Explicație pas cu pas:

$f(x) = 5-x$

a)

$f(1) + f(2) + f(3) + ... + f(100) = (5 - 1) + (5 - 2) + (5 - 3) + ... + f(5 - 100) = 5 - 1 + 5 - 2 + 5 - 3 + ... + 5 - 100 = 5 \times 100 - (1 + 2 + 3 + ... + 100) = 500 - \frac{100 \times 101}{2} = 500 - 5050 = - 4550$

b)

$f(5) = 5 - 5 = 0$

$f(1) \times f(2) \times f(3) \times f(4) \times f(5) \times ...\times f(100) = f(1) \times f(2) \times f(3) \times f(4) \times 0 \times ...\times f(100) = 0$