Question

2) Determine a função inversa de:


a) y = 3x - 5

b) y = - 4x + 7

c) y = 3 + 2x

d) y = x³ + 4


ajudaaaaaaaa

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm Para\,obter\,a\,func_{\!\!,}\tilde ao\,inversa:}\\\sf 1^o~isole~x\\\sf 2^o~troque\,x\,por\,y.\end{array}}$

$\large\boxed{\begin{array}{l}\tt a)~\sf y=3x-5\\\sf 1^o~isole\,x:\\\sf y=3x-5\\\sf 3x-5=y\\\sf 3x=y+5\\\sf x=\dfrac{y+5}{3}\\\sf 2^o~troque\,x\,por\,y:\\\sf y=\dfrac{x+5}{3}\end{array}}$

$\large\boxed{\begin{array}{l}\tt b)~\sf y=-4x+7\\\sf 1^o~isole\,x:\\\sf -4x+7=y\\\sf 4x=7-y\\\sf x=\dfrac{7-y}{4}\\\\\sf 2^o\,troque\,x\,por\,y:\\\sf y=\dfrac{7-x}{4}\end{array}}$

$\large\boxed{\begin{array}{l}\tt c)~\sf y=3+2x\\\sf 1^o~isole\,x:\\\sf 3+2x=y\\\sf 2x=y-3\\\sf x=\dfrac{y-3}{2}\\\\\sf 2^o~troque\,x\,por\,y:\\\sf y=\dfrac{x-3}{2}\end{array}}$

$\large\boxed{\begin{array}{l}\tt d)~\sf y=x^3+4\\\sf 1^o\,isole\,x:\\\sf x^3+4=y\\\sf x^3=y-4\\\sf x=\sqrt[\sf3]{\sf y-4}\\\sf 2^o~troque~x~por~y:\\\sf y=\sqrt[\sf3]{\sf x-4}\end{array}}$