Question

de a funcao inversa:

a)  y=x+9

b)  y=5x

c)  y=2x+5

Answer 1

$a)\\f(x)=x+9\\\\y=x+9\\x=y+9\\y=x-9\\\\\boxed{f(x)^{-1}=x-9}$

$b)\\\\y=5x\\x=5y\\y=\frac{x}{5}\\\\\boxed{f(x)^{-1}=\frac{x}{5}}$

$c)\\\\y=2x+5\\x=2y+5\\y=\frac{x-5}{2}\\\\\boxed{f(x)^{-1}=\frac{x-5}{2}}$

Obs: Para achar a inversa , basta substituir y por x e depois isolar o y , ex:

$y=ax$

Utilizando a técnica :

$x=ay$

a inversa séra :

$y=\frac{x}{a}$