Question

15. (Uece) Seja f(x) = 1/x, x · 0. Se f(2+p) - f(2) = 3/2, então f(1 - p) - f(1+p) é igual a: a) 8/5 b) 2 c) 12/5 d) 20/3? heeelllpppp :)

Answer 1

Temos que:

$f(x) = \frac{1}{x}$

Assim:

$f(2+p) - f(2) = \frac{3}{2} \\ \\ \frac{1}{2 + p} - \frac{1}{2} = \frac{3}{2} \\ \\ \frac{2 - (2 + p)}{2(2 + p)} = \frac{3}{2} \\ \\ \frac{-p}{2(2 + p)} = \frac{3}{2} \\ \\ -p = 3( 2 + p) \\ \\ -p = 6 + 3p \\ \\ 4p = -6 \\ \\ p = - \frac{6}{4} = - \frac{3}{2}$

Logo:

$f(1-p) - f(1 + p) = f(1 - ( -\frac{3}{2})) - f(1 - \frac{3}{2}) = f(1 + \frac{3}{2}) -f(1 - \frac{3}{2}) \\ \\ = f( \frac{5}{2} ) - f( -\frac{1}{2} )\\ \\ = \frac{1}{ \frac{5}{2} } - \frac{1}{ -\frac{1}{2} } \\ \\ = \frac{2}{5} - (- 2) \\ \\ = \frac{2}{5} + 2 \\ \\ = \frac{12}{5}$