Question

(MACK) Os gráficos das funções reais definidas por f(x) = x² - 1 e g(x) = kx, 1 ¹ k > 0, se interceptam num ponto de abscissa 3. Então o valor de f(g(k)) é:
a) 3                  b) 9                  c) 12                d) 15                e) 18

Answer 1

$\left \{ {f(x) = x^2 - 1} \atop {g(x) = k^{x} -> g(k) = k^{k} }} \right.$

$3^2 - 1 = K^{3} 9 - 1 = K^{3} 8 = K^{3} K = \sqrt[3]{8} K = 2$

$f(g(k)) = ( K^{k} )^2 - 1 f(g(k)) = ( 2^{2} )^2 - 1 f(g(k)) = 2^4 - 1 f(g(k)) = 16 - 1 f(g(k)) = 15$