Question

(puc-rs) seja a função f: r -> r tal que f(3x+1) = 1 - x então f(a) é

Answer 1

$f(x)=mx+n$

$f(3x+1)=m*(3x+1)+n$

$f(3x+1)=3mx+m+n$

$1-x=3mx+m+n$

$3m=-1$

$\boxed{m=-\frac{1}{3}}$

$m+n=1$

$-\frac{1}{3}+n=1$

$\boxed{n=\frac{4}{3}}$

$f(x)=-\frac{1}{3}*x+\frac{4}{3}$

desta forma

$\boxed{\boxed{f(a)=-\frac{1}{3}*a+\frac{4}{3}}}$