Question

Determine a função inversa de cada função
dada por:
a) y = 4x + 2
b) y = x+2/x-2
c)y=x-4/x+1​

Answer 1

Resposta:

Olá.

Primeiramente substituímos o termo x por y;

$a)y=4x+2\\x=4y+2\\4y=x-2\\y=\frac{x}{4}-\frac{2}{4}\\\boxed{y=\frac{x}{4}-\frac{1}{2}}\\\\f(x)^{-1}=\frac{x}{4}-\frac{1}{2}\\\\b)y=\frac{x+2}{x-2}\\x=\frac{y+2}{y-2}\\x*(y-2)=y+2\\xy-2x=y+2\\isolando;\\xy-y=2x+2\\y*(x-1)=2x+2\\\boxed{y=\frac{2x+2}{x-1}}\\\\f(x)^{-1}=\frac{2x+2}{x-1}\\\\\\c)y=\frac{x-4}{x+1}\\x=\frac{y-4}{y+1}\\x*(y+1)=y-4\\xy+x=y-4\\xy-y=-x-4\\y*(x-1)=-x-4\\y=\frac{-x-4}{x-1}\\\\f(x)^{-1}=\frac{-x-4}{x-1}$

Explicação passo-a-passo: