Question

dada a função cálcule: ​

Answer 1

Resposta:

$f^-^1(x)=\frac{3x+1}{x-2},~~x\neq 2\\\\f^-^1(-4)=\frac{11}{6}$

Explicação passo-a-passo:

f(x) = y

$y=\frac{2x+1}{x-3}\\\\Permutando ~~as~~vari\'aveis\\\\x=\frac{2y+1}{y-3}\\\\x(y-3)=2y+1\\\\xy-3x=2y+1\\\\xy-2y=1+3x\\\\y(x-2)=3x+1\\\\y=\frac{3x+1}{x-2}\\\\f^-^1(x)= \frac{3x+1}{x-2},~~x\neq 2 \\\\b)f^-^1(-4)=\frac{3(-4)+1}{-4-2} =\frac{-11}{-6}=\frac{11}{6}$

Answer 2

a) na imagem:

1° colocar x no lugar do y, e y no lugar do x.

2° insola x.

b) f-¹ (x) = (1+3x)/(x–2)

f-¹ (–4) = (1+3•(–4))/((–4)–2)

f-¹ (–4) = (1+(–12))/(–6)

f-¹ (–4) = (1 –12)/(–6)

f-¹ (–4) = (–11)/(–6) (faz jogo de sinal, sinais iguais fica positivo)

f-¹ (–4) = 11/6

ou f-¹ (–4) = 1,83