Question

Determine a função inversa:
A)y=5x-4/2
B)y=2x+8/3x-1
C)y=5x/3
D)y=-x+2/3

Answer 1

a)
$y= \frac{5x-4}{2} \\ x= \frac{5y-4}{2} \\ 2x=5y-4 \\ 5y=2x+4 \\ y= \frac{2x+4}{5} \\ \\ f^{-1}(x)= \frac{2x+4}{5}$

b)
$y=\frac{2x+8}{3x-1} \\ x= \frac{2y+8}{3y-1} \\ x(3y-1)=2y+8 \\ 3xy-x=2y+8 \\ 3xy-2y=8+x \\ y(3x-2)=8+x \\ y= \frac{8+x}{3x-2} \\ \\ f^{-1}(x) = \frac{x+8}{3x-2}$

c)
$y= \frac{5x}{3} \\ x= \frac{5y}{3} \\ 3x=5y \\ y= \frac{3x}{5} \\ \\ f^{-1}(x)= \frac{3x}{5}$

d)
$y= \frac{-x+2}{3} \\ x= \frac{-y+2}{3} \\ 3x=-y+2 \\ y=2-3x \\ \\ f^{-1}(x)=-3x+2$