Question

Eu pago a quem responder essas questões pra mim... Cliquem na pergunta que aparece a foto!

Answer 1

Resposta:

Vide explicação

Explicação passo-a-passo:

1)

$f(x+x) = f(x) + f(y)$

Podemos verificar isso na função identidade:

$f(x) = x$

Então f(0) = 0

f(0) + 1 = 1

2)

$f(x) = x^2+2x+1\\g(x) = x + 3\\f(g(x)) = (x + 3)^2+2(x + 3)+1\\f(g(x)) = x^2 + 6x +9 +2x+6+1\\\\f(g(x)) = x^2 + 8x+16$

3)

$f(x) = \frac{2}{x-1}\\\\ f(2) = \frac{2}{2-1} = 2 \\\\\sqrt{8f(f(2))} \rightarrow \sqrt{8f(2)}\\\\\sqrt{8\cdot 2} = \sqrt{16} = 4\\\\\sqrt{8f(f(2))} = 4$

4)

$f(x) = \frac{x+2}{4}\\\\f^{-1}(x) = \frac{y+2}{4}\\\\x = \frac{y+2}{4}\\\\4x = y+2\\\\y = 4x - 2\\\\f^{-1}(x) = 4x - 2\\\\\\f^{-1}(1) = 4.1 - 2\\f^{-1}(1) = 4 - 2\\\\f^{-1}(1) = 2$

5)

$f(x) = -5x+20\\\\-5x+20>0\\-5x > -20\\x > \frac{20}{5} = 4\\\\x > 4$