Question

Se f(x) = (8x-7)/(5x+8) esta definida para todo x E R - {-8/5}, entao o valor de f^-1(1) é:
a)-5
b)6
c)4
d)5
e)-6

Answer 1

$y=\frac { 8x-7 }{ 5x+8 } \\ \\ x=\frac { 8y-7 }{ 5y+8 } \\ \\ 5xy+8x=8y-7\\ 5xy-8y=-8x-7\\ y(5x-8)=-8x-7\\ y=\frac { -8x-7 }{ 5x-8 } \\ \\ f^{ -1 }=\frac { -8x-7 }{ 5x-8 } \\ \\ f^{ -1 }(1)=\frac { -8(1)-7 }{ 5(1)-8 } \\ \\ f^{ -1 }(1)=\frac { -15 }{ -3 } \\ \\ f^{ -1 }(1)=5$

R:D