Question

Determine (fog) (x) y gof) (x) si : f(x)= 1-4x+x2 g (x) 3 raiz cuadrada 3x

Answer 1

$f(x) = 1 - 4x + {x}^{2} \\ g(x) = 3 \sqrt{3x} \\ (fog)(x) = f(g(x)) \\ = f(3 \sqrt{3x} ) = 1 - 4 \times 3 \sqrt{3x} + {(3 \sqrt{3x}) }^{2} \\ = 1 - 12 \sqrt{3x} + 9 \times 3x \\ = 1 - 12 \sqrt{3x} + 27x$
$(gof)(x) = g(f(x)) \\ = g(1 - 4x + {x}^{2} ) \\ = 3 \sqrt{3(1 - 4x + {x}^{2}) } \\ = 3 \sqrt{3 - 12x + 3 {x}^{2} }$