Question

ATIVIDADE DE MATEMÁTICA 2 QUESTÕES

Answer 1

41)

$a) \\ y= \frac{2x+1}{x+9} \\ \\ y(x+9)=2x+1 \\ \\ yx+9y=2x+1 \\ \\ yx-2x=1-9y \\ \\ x(y-2)=1-9y \\ \\ x= \frac{1-9y}{y-2} \\ \\ x= \frac{9y-1}{2-y} \\ \\ f^{-1} (x) = \frac{9y-1}{2-y}$

substituindo x=y

$f^{-1} (x)= \frac{9x-1}{2-x}$

$b) \\ D_{f} =( - \infty},-9)U(9,+\infty) \\ \\ x+9 \neq 0 \\ \\ x \neq -9$

$c) \\ D_{ f^{-1} } =(-\infty,2)U(2,+\infty) \\ \\ 2-x \neq 0 \\ \\ -x \neq -2 \\ \\ x \neq 2$

$d) \\ Im(f)= D_{ f^{-1} } =(-\infty,2)U(2,+\infty)$

$e) \\ Im( f^{-1} )= D_{f} =(-\infty,-9)U(-9,+\infty)$

$42) \\ a) \\ y=4x+9 \\ \\ -4x=-y+9 \\ \\ 4x=y-9 \\ \\ x= \frac{y-9}{4}$

$b) \\ y=-2x+3 \\ \\ 2x=-y+3 \\ \\ x= \frac{-y+3}{2}$

$c) \\ y=-7x- \frac{1}{2} \\ \\ 7x=-y- \frac{1}{2} \\ \\ x= \frac{-y- \frac{1}{2} }{7} \\ \\ x= \frac{ \frac{-2y-1}{2} }{7} \\ \\ x= \frac{-2x-1}{14}$

$d) \\ y= \frac{x+5}{3} \\ \\ 3y=x+5 \\ \\ -x=-3y+5 \\ \\ x=3y-5$

$e) \\ y=x^3+1 \\ \\ -x^3=-y+1 \\ \\ x^3=y-1 \\ \\ x= \sqrt[3]{y-1}$

$f) \\ y= \sqrt[5]{2x} \\ \\ y^{5} =(( 2x^{ \frac{1}{5} } )^5 \\ \\ y^{5} = 2x^{1} \\ \\ y^{5} =2x \\ \\ x= \frac{ y^{5} }{2}$