Question

Se g é uma função tal que g(3x − 1) = x² − 4 para todo x ∈ R, determine:g(14) + 9g(0).

Answer 1

Resposta:

38

Explicação passo a passo:

g(3x − 1) = x² − 4

Seja 3x - 1 = a

3x = a + 1

$x=\frac{a+1}{3} \\\\g(a) =(\frac{a+1}{3})^2-4\\\\g(a)=\frac{a^2+2a+1}{3}-4\\\\g(x) =\frac{x^2+2x+1}{3}-4\\\\g(14)=\frac{14^2+2.14+1}{3}-4\\\\g(14)=\frac{196+29}{3}-4\\\\g(14)=\frac{225}{3}-4\\\\ g(14)=75-4=71\\\\g(0)=\frac{0^2+2.0+1}{3}-4\\\\g(0)=\frac{1}{3}-4=-\frac{11}{3} \\\\f(14) +9.g(0)=71+9.(-\frac{11}{3} )=71-3.11 =71-33=38$