Question

f(x)=1/x sa se calculeze suma
S=f(f(-10))+f(f(-9)+...+f(f(-1))+f(f(1))+...+f(f(9)+f(f(10))​

Answer 1

Răspuns:

S = 0

Explicație pas cu pas:

$f( - 10) = - \frac{1}{10} \\ f(f( - 10) = \frac{1}{ - \frac{1}{10} } = - 10 \\f( - 9) = - \frac{1}{9} \\ f(f( - 9) = \frac{1}{ - \frac{1}{9} } = - 9 \\ ... \\ f( - 1) = - \frac{1}{1} = -1 \\ f(f( - 1) = \frac{1}{ - 1} = - 1\\ f(1)= \frac{1}{1}=1\\f(f(1)= \frac{1}{1} =1 \\ f(9) =\frac{1}{9} \\ f(f(9) = \frac{1}{\frac{1}{9} } =9 \\ f(10) = \frac{1}{10} \\ f(f(10) = \frac{1}{\frac{1}{10} } = 10$

$S = (- 10) + ( - 9) + ... + ( - 1) + 1 + ... + 9 + 10 = 0$