Jika f(x) = 1/x+1 dan g(x) = 2/3-x' maka fungsi ( f o g ) ^-1 (3)= Mohon bantuanya lagi...

Matematika

[tex]f(x) = \frac{1}{x + 1} \\ g(x) = \frac{2}{3 - x} [/tex]

[tex](fog)(x) = f(g(x)) \\ = \frac{1}{g(x) + 1} \\ = \frac{1}{ \frac{2}{3 - x} + 1} \\ = \frac{1}{ \frac{5 - x}{3 - x} } \\ = \frac{3 - x}{5 - x} [/tex]

[tex]y = \frac{3 - x}{5 - x} \\ y(5 - x) = 3 - x \\ 5y - xy = 3 - x \\ xy - x = 5y - 3 \\ x(y - 1) = 5y - 3 \\ x = \frac{5y - 3}{y - 1} [/tex]

[tex] {(fog)}^{ - 1}(x) = \frac{5x - 3}{x - 1} \\ \\ {(fog)}^{ - 1} (3) = \frac{5(3) - 3}{3 - 1} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{12}{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 6[/tex]