Question

seja as funçoes g(x)=3x+2 fog(x)=x^-x+1.Determine a expressao de f.​

Answer 1

Resposta:

$f(x)=\frac{x^2}{9}-\frac{7x}{9}+\frac{19}{9}$

Explicação passo a passo:

g(x) = 3x + 2 e f0g(x) = x² - x + 1

f0g(x) = f(g(x))  

f(g(x)) = x² - x +1

f(3x + 2) =  x² - x + 1

fazendo 3x + 2 = a

3x = a - 2

$x=\frac{a-2}{3}$

f(3x + 2) =  x² - x + 1

$f(a)=(\frac{a-2}{3})^2 -\frac{a-2}{3} +1\\\\f(a)=\frac{a^2-4a+4}{9} -\frac{a-2}{3} +1\\\\f(a)=\frac{a^2-4a+4-3a+6+9}{9} \\\\f(a)=\frac{a^2-7a+19}{9} \\\\f(a)=\frac{a^2}{9}-\frac{7a}{9} +\frac{19}{9} \\\\Subst~~a~por~x\\\\f(x)=\frac{x^2}{9}-\frac{7x}{9}+\frac{19}{9}$