Question

me salvem glrrr, pfvrrr​

Answer 1

f(x) = a . x + b

f(a) = 2b

f(a) = a. a + b

f(a) = a² + b

2 b = a² + b

2 b - b = a²

b = a²

f(b) = 2a

f(b) = a . b + b

2a = a . b + b

2a - a . b = b

a (2 - b) = b

$a = \frac{b}{2-b}$

Substituindo

b = a²

b = ${\frac{b}{2-b} }^2$

$b . (2-b)^2=b^2$

$b . (b^2 - 4b + 4) = b^2$

$b^3-4b^2+4b-b^2=0$

$b^3-5b^2+4b=0$

$b.(b^2-5b+4)=0\\b = 0\\b^2-5b+4 = 0$

Δ=$b^2-4.a.c$

Δ=$(-5)^2-4.1*4$

Δ= 25 - 16

Δ= 9

$x = \frac{-b+-\sqrt{\Delta} }{2.a}$ (não consegui colocar o sinal de + ou - junto)

$x = \frac{-(-5)+-\sqrt{9} }{2.1}$

$x = \frac{5+-3 }{2}$

$x' = \frac{5-3 }{2}$

$x' = \frac{2}{2}$

$x' = 1$

$x'' = \frac{5+3 }{2}$

$x'' = \frac{8 }{2}$

$x'' = 4$

Resposta: letra b)