Question

Considere a função f(x) = kx - 5. Se f(f(1)) = 19. A soma dos possíveis valores de k é:

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Answer 1

$\displaystyle \text {f(x)}=\text k.\text x-5 \ \ ; \ \ \text{f(f(1))}=19 \\\\ \text{Fa{\c c}amos}: \\\\ \text{f(1)}= \text k.1-5 \\\\ \text{f(f(1))} =\text k(\text k-5)-5 \\\\ 19=\text k^2-5\text k-5 \\\\ \text k^2-5\text k-5-19=0 \\\\ \text k^2-5\text k-24=0 \\\\ \text a = 1 \ , \ \text b=-5\ ,\ \text c=-24 \\\\ \underline{\text{Soma dos valores de de k que satisfazem a equa{\c c}{\~a}o}}: \\\\ \text k_1+\text k_2 = \frac{-\text b}{\text a}= \frac{-(-5)}{1} = \huge\boxed{5}$